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BEGIN:VEVENT
SUMMARY:Gaia Comaschi (University of Campinas)
DTSTART;VALUE=DATE-TIME:20200415T183000Z
DTEND;VALUE=DATE-TIME:20200415T193000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/1
DESCRIPTION:Title: GIT
stability of linear systems of skew-symmetric forms\nby Gaia Comaschi
(University of Campinas) as part of Brazilian algebraic geometry seminar\
n\n\nAbstract\nGiven a 6 dimensional vector space $W$\, we consider $\\mat
hbb{P}(\\mathbb{C}^{n+1}\\otimes \\bigwedge ^2 W^*)$\, the projective spac
e parameterizing n-dimensional linear systems of skew-symmetric forms on $
W$. Since the group $SL(W)$ acts on $\\mathbb{P}(\\mathbb{C}^{n+1}\\otimes
\\bigwedge ^2 W^*)$\, Geometric Invariant Theory (GIT) provides a notion
of (semi)stability. In this talk I will introduce a criterion to detect th
e (semi)stability of linear systems of skew-symmetric forms and I will the
n present how this criterion allows to obtain a complete classification of
all stable linear systems having generic rank equal to 4.\n\nAccess the Z
oom link\nhttps://zoom.us/j/92887438541?pwd=Q3BHRU9CcFBicTJ1eXhacVpLOERKUT
09\n
LOCATION:https://researchseminars.org/talk/BRAG/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giosuè Muratore (Federal University of Minas Gerais (UFMG))
DTSTART;VALUE=DATE-TIME:20200429T183000Z
DTEND;VALUE=DATE-TIME:20200429T193000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/2
DESCRIPTION:Title: A R
ecursive Formula for Osculating Curves\nby Giosuè Muratore (Federal U
niversity of Minas Gerais (UFMG)) as part of Brazilian algebraic geometry
seminar\n\n\nAbstract\nLet $X$ be a smooth complex projective variety. Usi
ng a construction\ndevised to Gathmann\, we present a recursive formula fo
r some of the\nGromov-Witten invariants of $X$. We prove that\, when $X$ i
s homogeneous\, this\nformula gives the number of osculating rational curv
es at a general point of a general hypersurface of $X$. This generalizes t
he classical well known pairs of in inflection (asymptotic) lines for surf
aces in $\\mathbb{P}^3$ of Salmon\, as well as Darboux's 27 osculating con
ics.\n\nLink for the talk will be provided a few days in advance.\n
LOCATION:https://researchseminars.org/talk/BRAG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas das Dores (IMPA)
DTSTART;VALUE=DATE-TIME:20200422T183000Z
DTEND;VALUE=DATE-TIME:20200422T193000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/3
DESCRIPTION:Title: Sch
emes of rational curves on Del Pezzo surfaces\nby Lucas das Dores (IMP
A) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nSchemes
parametrizing rational curves on a projective variety have a natural parti
tion in terms of the degrees of the rational curves. In this talk\, we pre
sent a natural refinement of this partition on schemes parametrizing ratio
nal curves on Del Pezzo surfaces. The classical description of Del Pezzo s
urfaces as blow-ups of the projective plane at points in general position
yields that these refined partitions reflect the multiplicity of the ratio
nal curves at each of the blown-up points. Moreover\, we compute the dimen
sion of components of these parameter spaces containing (points correspond
ing to) resolutions of plane curves which are singular at the blown-up poi
nts.\n
LOCATION:https://researchseminars.org/talk/BRAG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ugo Bruzzo (SISSA/UFPB)
DTSTART;VALUE=DATE-TIME:20200513T183000Z
DTEND;VALUE=DATE-TIME:20200513T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/5
DESCRIPTION:Title: Abo
ut the McKay correspondence in 3 dimensions\nby Ugo Bruzzo (SISSA/UFPB
) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nAbstract:
I will review work on the McKay correspondence in 3 dimensions and its di
fferential-geometric version\, relying on papers by Ito-Reid\, Sardo Infir
ri\, Craw-Ishi and others\, and on some original results obtained with a g
roup of collaborators. This is about the resolution of singularities of th
e type C^3/G\, where G is a finite subgroup of GL(3\,C) or SL(3\,C). I wil
l also discuss the chamber structure for the stability parameter of the GI
T quotient. I will illustrate the general theory by means of a nontrivial
but manageable example (C^3/Z_4 with Z_4 acting as a subrgoup of SL(3\,C))
. I will also hint at some physical motivations.\n\nLink for the Zoom meet
ing: https://us02web.zoom.us/j/84979113106?pwd=ZTc5c0N4WCtVdmdqbHNiMzhiQU8
2QT09\n
LOCATION:https://researchseminars.org/talk/BRAG/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Almeida (Federal University of Minas Gerais (UFMG))
DTSTART;VALUE=DATE-TIME:20200520T183000Z
DTEND;VALUE=DATE-TIME:20200520T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/6
DESCRIPTION:Title: The
geography of moduli spaces of torsion free sheaves\nby Charles Almeid
a (Federal University of Minas Gerais (UFMG)) as part of Brazilian algebra
ic geometry seminar\n\n\nAbstract\nIn this talk I will describe new irredu
cible components of the moduli space of rank 2 semistable torsion free she
aves on the 3-dimensional projective space\, whose generic point correspon
ds to non-locally free sheaves. As an application\, I will compute the num
ber of irreducible components of the moduli space of torsion free sheaves\
, with first\, second and third Chern classes equal to -1\, 2 and 2 respec
tively. Additionaly\, I will give an idea of how to prove that this moduli
space is connected. This is a joint work with Marcos Jardim and Alexander
S. Tikhomirov.\n
LOCATION:https://researchseminars.org/talk/BRAG/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Fonseca (University of Oxford)
DTSTART;VALUE=DATE-TIME:20200603T183000Z
DTEND;VALUE=DATE-TIME:20200603T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/7
DESCRIPTION:Title: Fro
m transcendental numbers to higher Ramanujan foliations\nby Tiago Fons
eca (University of Oxford) as part of Brazilian algebraic geometry seminar
\n\n\nAbstract\nI will explain how a problem in the theory of transcendent
al numbers leads to the construction of certain principal bundles over mod
uli stacks of abelian varieties. Such bundles carry a natural horizontal f
oliation whose corresponding differential equations generalize Ramanujan's
classical relations between Eisenstein series. I will then discuss a resu
lt on the Zariski-density of the analytic leaves of this foliation.\n\nGoo
gle meet link https://meet.google.com/wwv-sajj-fsn\n
LOCATION:https://researchseminars.org/talk/BRAG/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Vitório Pereira (IMPA)
DTSTART;VALUE=DATE-TIME:20200527T183000Z
DTEND;VALUE=DATE-TIME:20200527T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/8
DESCRIPTION:Title: Miy
aoka's algebraicity criterion and variations\nby Jorge Vitório Pereir
a (IMPA) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nI
will review some old and new results/arguments on the \nalgebraicity of le
aves of foliations with "positive" tangent \nsheaf.\n\nLink for google mee
t will be posted a few days in advance.\n
LOCATION:https://researchseminars.org/talk/BRAG/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Herivelto Borges\, Saeed Tafazolian\, Luciane Quoos Conte and Cíc
ero Carvalho (Federal University of Minas Gerais (UFMG))
DTSTART;VALUE=DATE-TIME:20200610T183000Z
DTEND;VALUE=DATE-TIME:20200610T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/9
DESCRIPTION:Title: In
honor of Fernando Torres\nby Herivelto Borges\, Saeed Tafazolian\, Luc
iane Quoos Conte and Cícero Carvalho (Federal University of Minas Gerais
(UFMG)) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nOur
esteemed colleague Fernando Torres passed away on May 28th 2020\, aged 58
. He completed his PhD at IMPA in 1993 under the supervision of Arnaldo Ga
rcia\, and was a professor at the University of Campinas since 1998. He wa
s widely known for his many contributions to the theory of algebraic curve
s over finite fields and its applications.\n\nThis memorial session will h
ave short presentations by Herivelto Borges\, Saeed Tafazolian\, Luciane Q
uoos Conte and Cícero Carvalho and completed with testimonies by Arnaldo
Garcia\, and Torres's students\, collaborators and friends.\n\nLink for go
ogle meet: meet.google.com/bve-gahp-ocn\n
LOCATION:https://researchseminars.org/talk/BRAG/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cecília Salgado (Federal University of Rio de Janeiro (UFRJ))
DTSTART;VALUE=DATE-TIME:20200624T183000Z
DTEND;VALUE=DATE-TIME:20200624T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/10
DESCRIPTION:Title: Mo
rdell-Weil rank jumps and the Hilbert property\nby Cecília Salgado (F
ederal University of Rio de Janeiro (UFRJ)) as part of Brazilian algebraic
geometry seminar\n\n\nAbstract\nLet X be an elliptic surface with a secti
on defined over a number field. Specialization theorems by Néron and Silv
erman imply that the rank of the Mordell-Weil group of special fibers is a
t least equal to the MW rank of the generic fiber. We say that the rank ju
mps when the former is strictly larger than the latter. In this talk\, I w
ill discuss rank jumps for elliptic surfaces fibred over the projective li
ne. If the surface admits a conic bundle we show that the subset of the li
ne for which the rank jumps is not thin in the sense of Serre. This is joi
nt work with Dan Loughran (Bath).\n\nLink for the google meet will be post
ed here a few days before the talk.\n
LOCATION:https://researchseminars.org/talk/BRAG/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Genival da Silva Junior (Imperial College)
DTSTART;VALUE=DATE-TIME:20200617T183000Z
DTEND;VALUE=DATE-TIME:20200617T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/11
DESCRIPTION:Title: Su
rfaces with Exceptional monodromy\nby Genival da Silva Junior (Imperia
l College) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\n
There have been several constructions of family of varieties with exceptio
nal monodromy group. In most cases\, these constructions give Hodge struct
ures with high weight(Hodge numbers spread out). N. Katz was the first to
obtain Hodge structures with low weight(Hodge numbers equal to (2\,3\,2))
and geometric monodromy group G2. I this talk I will give an alternate des
cription of Katz's result using Hodge theory.\n
LOCATION:https://researchseminars.org/talk/BRAG/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:André Contiero (Federal University of Minas Gerais (UFMG))
DTSTART;VALUE=DATE-TIME:20200701T183000Z
DTEND;VALUE=DATE-TIME:20200701T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/12
DESCRIPTION:Title: Cu
rves and Weierstrass points\nby André Contiero (Federal University of
Minas Gerais (UFMG)) as part of Brazilian algebraic geometry seminar\n\n\
nAbstract\nIn this talk we will present some working in progress on the mo
duli space of pointed curves with prescribed Weierstrass semigroup at the
marked point. We will present a tight lower bound for its dimension when t
he semigroup is non-negatively graded\, and we will also give sufficient c
ondition to its rationality when the semigroup is symmetric.\n\nLink for g
oogle meet will be posted here a few days in advance.\n
LOCATION:https://researchseminars.org/talk/BRAG/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amar Henni (Federal University of Santa Catarina (UFSC))
DTSTART;VALUE=DATE-TIME:20200722T183000Z
DTEND;VALUE=DATE-TIME:20200722T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/13
DESCRIPTION:Title: On
the fixed locus of framed instanton sheaves on $\\mathbb{P}^3$\nby Am
ar Henni (Federal University of Santa Catarina (UFSC)) as part of Brazilia
n algebraic geometry seminar\n\n\nAbstract\nLet T be the three dimensional
torus acting on $\\mathbb{P}^3$ and MT(c) be the fixed locus of the corre
sponding action on the moduli space of rank 2 framed instanton sheaves on
$\\mathbb{P}^3$. We show that MT(c) consist only of non locally-free insta
nton sheaves whose double dual is the trivial bundle. Moreover\, we relate
these instantons to multiple structures and give a classification of thei
r support. This allows to compute a lower bound on the number of component
s of MT(c).\n\nLink for the google meet will be posted here a few days bef
ore the talk.\n
LOCATION:https://researchseminars.org/talk/BRAG/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Richster (Federal University of Itajubá (UNIFEI))
DTSTART;VALUE=DATE-TIME:20200708T183000Z
DTEND;VALUE=DATE-TIME:20200708T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/14
DESCRIPTION:Title: Se
cant defectiveness of toric varieties\nby Rick Richster (Federal Unive
rsity of Itajubá (UNIFEI)) as part of Brazilian algebraic geometry semina
r\n\n\nAbstract\nThe $h$-secant variety $Sec_{h}(X)$ of a non-degenerate $
n$-dimensional variety $X\\subset\\mathbb{P}^N$ is the Zariski closure of
the union of all linear spaces spanned by collections of $h$ points of $X$
.\nThe expected dimension of $Sec_{h}(X)$ is \n$Expdim(Sec_{h}(X)):= \\min
\\{nh+h-1\,N\\}$.\nThe actual dimension of $Sec_{h}(X)$ may be smaller tha
n the expected one. \n\nLet $N$ be a rank $n$ free abelian group and $M$ i
ts dual. Let $P\\subseteq M_{\\mathbb Q}$ be a full dimensional lattice po
lytope and $X_P$ the corresponding toric variety.\n\nIn this talk we discu
ss a new technique to give bounds on the Secant Defectivity of $X_P$ using
information from the polytope $P$. It is a joint work just submitted with
Antonio Laface and Alex Massarenti.\n\nThe link for the google meet will
be posted here a few days in advance.\n
LOCATION:https://researchseminars.org/talk/BRAG/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maral Mostafazadehfard (Federal University of Rio de Janeiro (UFRJ
))
DTSTART;VALUE=DATE-TIME:20200715T183000Z
DTEND;VALUE=DATE-TIME:20200715T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/15
DESCRIPTION:Title: Di
visor class group of Hankel determinantal rings\nby Maral Mostafazadeh
fard (Federal University of Rio de Janeiro (UFRJ)) as part of Brazilian al
gebraic geometry seminar\n\n\nAbstract\nHankel determinantal rings arise a
s homogeneous coordinate rings of higher order secant varieties of rationa
l normal curves. In any characteristic we give an explicit description of
divisor class groups of these rings and as a consequence we show that they
are $\\mathbb{Q}$-Gorenstein rings. It has been shown that each divisor c
lass group element is the class of a maximal Cohen Macaulay module.\n\nBas
ed on a joint work with Aldo Conca\, Anurag K. Singh and Matteo Varbaro.\n
LOCATION:https://researchseminars.org/talk/BRAG/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rodrigo Gondim (UFRPe)
DTSTART;VALUE=DATE-TIME:20200812T183000Z
DTEND;VALUE=DATE-TIME:20200812T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/16
DESCRIPTION:Title: Wa
ring problems and the Lefschetz properties\nby Rodrigo Gondim (UFRPe)
as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nWe study th
ree variations of the Waring problem for homogeneous polynomials\, concern
ing the Waring rank\, the border rank and the cactus rank of a form. We sh
ow how the Lefschetz properties of the associated algebra affect them. The
main tool is the theory of mixed Hessians and Macaulay-Matlis duality. We
construct new families of wild forms\, that is\, forms whose cactus rank\
, of schematic nature\, is bigger then the border rank\, defined geometric
ally.\n(Joint with T. Dias)\n
LOCATION:https://researchseminars.org/talk/BRAG/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Villaflor (IMPA)
DTSTART;VALUE=DATE-TIME:20200805T183000Z
DTEND;VALUE=DATE-TIME:20200805T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/17
DESCRIPTION:Title: Co
nstructing algebraic cycles on hypersurfaces\, an explicit approach to Hod
ge conjecture\nby Roberto Villaflor (IMPA) as part of Brazilian algebr
aic geometry seminar\n\n\nAbstract\nHodge conjecture is one of the major c
onjectures in algebraic geometry. In all the cases where Hodge conjecture
has been verified\, no constructive proof has been given up to the date. I
n other words there is no hint about how to construct an algebraic cycle f
rom a given Hodge cycle. In this talk we will consider this problem in the
case of hypersurfaces of the projective space. We will explain how this q
uestion becomes more treatable when the Hodge cycle is given in a good eno
ugh format in terms of Griffiths basis. Reducing the problem to constructi
ng these nice representatives of Hodge cycles. We will see some examples w
here this approach works and highlight the difficulties that appear in the
general case.\n
LOCATION:https://researchseminars.org/talk/BRAG/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rodrigo Barbosa (Simons Center for Geometry and Physics)
DTSTART;VALUE=DATE-TIME:20200729T183000Z
DTEND;VALUE=DATE-TIME:20200729T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/18
DESCRIPTION:Title: St
ring Dualities\, Higgs Bundles and $G_2$ Geometry\nby Rodrigo Barbosa
(Simons Center for Geometry and Physics) as part of Brazilian algebraic ge
ometry seminar\n\n\nAbstract\nDualities in string/M theory often provide n
ovel perspectives for deformation problems in geometry. In one such instan
ce\, involving Large $N$ duality in the B-model\, one can construct a fami
ly of ALE-fibered Calabi-Yau threefolds over a Riemann surface $S_g$ ($g \
\geq 2$) whose Jacobian integrable system is isomorphic to the $G$-Hitchin
system over $S_g$\, where $G$ is the compact real form associated to the
ALE type via the McKay correspondence. I will explain a different physical
framework\, involving M-theory/Type IIA duality\, that gives an analogous
construction of ALE-fibered $G_2$-manifolds parametrized by spectral cove
rs of certain "smooth Higgs bundles" over a $3$-manifold. I will explain h
ow this theory connects with Donaldson's theory of Kovalev-Lefschetz fibra
tions and how it presents a window for applying algebro-geometric techniqu
es to moduli problems in $G_2$-geometry. Time permitting\, I will comment
on a second algebro-geometric model for the moduli space of (complexified)
$G_2$-structures derived from SYZ Mirror Symmetry for the Type IIA geomet
ry.\n
LOCATION:https://researchseminars.org/talk/BRAG/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Esteves (IMPA)
DTSTART;VALUE=DATE-TIME:20200902T183000Z
DTEND;VALUE=DATE-TIME:20200902T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/19
DESCRIPTION:Title: De
generations of line bundles along curves\nby Eduardo Esteves (IMPA) as
part of Brazilian algebraic geometry seminar\n\n\nAbstract\nA family of l
ine bundles along a family of smooth curves parameterized by the punctured
disk can be extended in several ways over the limit stable curve of the f
amily. We show that the collection of all extensions can be naturally para
meterized by the torus quotient of the arrangement of toric varieties asso
ciated to a certain polytope decomposition of a certain Euclidean space. W
e characterize all polytope decompositions arising this way in terms of co
mbinatorial data of the stable curve. At the end I will describe how these
results may be used to construct new compactifications of Jacobians of st
able curves and address the problem raised by Eisenbud and Harris of const
ructing a useful moduli of limit linear series over the moduli of stable c
urves. This is an ongoing joint work with Omid Amini (École Polytechnique
).\n
LOCATION:https://researchseminars.org/talk/BRAG/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nuno Cardoso / Aline Zanardini (University of Miami / University o
f Pennsylvania)
DTSTART;VALUE=DATE-TIME:20200826T183000Z
DTEND;VALUE=DATE-TIME:20200826T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/20
DESCRIPTION:Title: To
wards a new technique to compute Orlov spectra / Stability of Halphen penc
ils of index two\nby Nuno Cardoso / Aline Zanardini (University of Mia
mi / University of Pennsylvania) as part of Brazilian algebraic geometry s
eminar\n\n\nAbstract\nTowards a new technique to compute Orlov spectra\, b
y Nuno Cardoso \n\nAbstract: A generator of a triangulated category is an
object from which we can obtain the whole category through certain operati
ons. Associated to a generator\, there is the notion of the generation tim
e\, which is the number describing how long the rebuilding process takes.
The generation time of the fastest generator is called the Rouquier dimens
ion of the category and it is conjectured that the Rouquier dimension of t
he derived category of a smooth projective variety of dimension n is exact
ly n. Orlov suggested that in order to extract additional geometric inform
ation from the category\, one should study all possible generation times
– the Orlov spectrum. Later\, Ballard\, Favero and Katzarkov developed c
onsiderably our understanding of the topic\, making connections to rationa
lity\, computing the Orlov spectrum in several cases and finding bounds fo
r it. In this talk\, we will review part of their results and discuss our
work in progress on a new technique to compute the Orlov spectrum\, which
takes inspiration on Abouzaid's criterion for generating the Fukaya catego
ry in terms of open-closed maps.\n\n--xx--xx--\n\nStability of Halphen pen
cils of index two\, by Aline Zanardini\n\nAbstract: In this talk I will pr
esent some results about the stability\, in the sense of geometric invaria
nt theory\, of Halphen pencils of index two under the action of SL(3). The
se are pencils of plane curves of degree six having nine (possibly infinit
ely near) base points of multiplicity two. Inspired by the work of Miranda
on pencils of plane cubics\, I will explain how to explore the geometry o
f the associated rational elliptic surfaces. I will also show that the lo
g canonical threshold plays an important role. This work is part of my PhD
thesis at the University of Pennsylvania under the supervision of Antonel
la Grassi.\n
LOCATION:https://researchseminars.org/talk/BRAG/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Abreu (UFF)
DTSTART;VALUE=DATE-TIME:20200819T183000Z
DTEND;VALUE=DATE-TIME:20200819T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/21
DESCRIPTION:Title: A
geometric interpretation for characters of Iwahori--Hecke algebras\nby
Alex Abreu (UFF) as part of Brazilian algebraic geometry seminar\n\n\nAbs
tract\nThe Iwahori-Hecke algebra is a deformation of the group algebra of
the symmetric group. It has a distinguished basis (enumerated by permutati
ons) called the Kazhdan-Lusztig basis. For each permutation we consider c
ertain subvarieties of the complete flag variety that generalize Hessenber
g varieties. These varieties carry an action of the symmetric group on its
intersection cohomology groups. We prove that the Frobenius character of
this action is precisely the Frobenius character of an element of the Kaz
hdan-Lusztig basis of the Hecke algebra. This is a generalization to non-
codominant permutations of Brosnan-Chow's solution to the Sharesian-Wachs
conjecture. Some partial results in other Lie types are also achieved.\n
\nLink for the google meet will be posted here a few days before the talk.
\n
LOCATION:https://researchseminars.org/talk/BRAG/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Muniz (UFF)
DTSTART;VALUE=DATE-TIME:20200909T183000Z
DTEND;VALUE=DATE-TIME:20200909T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/22
DESCRIPTION:Title: On
moduli spaces of rank two logarithmic connections over an elliptic curve.
\nby Alan Muniz (UFF) as part of Brazilian algebraic geometry seminar\
n\n\nAbstract\nWe will give an explicit description of the (coarse) moduli
space of rank two logarithmic connections with fixed spectral data over a
n elliptic curve. Precisely\, we will show that this moduli space has a co
vering whose members are easily described.\n\nJoint work with Thiago Fassa
rella (UFF) and Frank Loray (IRMAR).\n
LOCATION:https://researchseminars.org/talk/BRAG/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Faenzi (Université de Bourgogne)
DTSTART;VALUE=DATE-TIME:20200916T183000Z
DTEND;VALUE=DATE-TIME:20200916T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/23
DESCRIPTION:Title: St
ability of logarithmic tangents\nby Daniele Faenzi (Université de Bou
rgogne) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nTo
a hypersurface $D$ of projective $N$-space $\\mathbb{P}^N$ one attaches th
e \\emph{log\ntangent sheaf} $T_D$ of vector fields of $\\mathbb{P}^N$ tan
gent to D. For some highly\nspecial hypersurfaces\, such as\, for instance
\, hyperplane arrangements\nassociated to reflection groups and discrimina
nts of binary forms\, the\nsheaf $T_D$ splits into line bundles - $D$ is
then called \\emph{free}. On the\nother hand\, Dolgachev--Kapranov proved
that $T_D$ is stable if $D$ is a\ngeneric arrangement of at least $N+2$ hy
perplanes\; also Dimca proved that\n$T_D$ is stable if $D$ has isolated si
ngularities with sufficiently small\nTjurina number and $N=3$.\n\nIn this
talk we will first show that $T_D$ is stable for a much wider\nclass of hy
persurfaces having low-dimensional singularities. In the\nsecond part of t
he talk we will prove that $T_D$ is stable if $D$ is the\ndeterminant of $
n\\times n$ matrices.\nIf time allows\, we will discuss the application fr
om the equisingular\nHilbert scheme containing $D$ to the moduli space of
semistable sheaves\ncontaining $T_D$ and show that it is birational in the
case of determinants.\n\nThis is a report on work in progress with S. Mar
chesi - soon on the arXiv.\n
LOCATION:https://researchseminars.org/talk/BRAG/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessia Mandini (UFF)
DTSTART;VALUE=DATE-TIME:20200923T183000Z
DTEND;VALUE=DATE-TIME:20200923T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/24
DESCRIPTION:Title: Qu
asi-parabolic Higgs bundles and null hyperpolygon spaces\nby Alessia M
andini (UFF) as part of Brazilian algebraic geometry seminar\n\n\nAbstract
\nHyperpolygons spaces are a family of hyperkähler manifolds\, that can b
e obtained from coadjoint orbits by hyperkähler reduction. Jointly with L
. Godinho\, we showed that these spaces are isomorphic to certain families
of parabolic Higgs bundles\, when a suitable condition between the parabo
lic weights and the spectra of the coadjoint orbits is satisfied.\n\nIn an
alogy to this construction\, we introduce two moduli spaces: the moduli sp
aces of quasi-parabolic $SL(2\,\\mathbb{C})$-Higgs bundles over $\\mathbb{
C}\\mathbb{P}^1$ on one hand and the null hyperpolygon spaces on the other
\, and establish an isomorphism between them.\n\nFinally we describe the f
ixed loci of natural involutions defined on these spaces and relate them t
o the moduli space of null hyperpolygons in the Minkowski 3-space.\n\nThis
is based on joint works with Leonor Godinho.\n
LOCATION:https://researchseminars.org/talk/BRAG/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sally Andria / César Hilário (UFF / IMPA)
DTSTART;VALUE=DATE-TIME:20200930T183000Z
DTEND;VALUE=DATE-TIME:20200930T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/25
DESCRIPTION:Title: An
explicit resolution of the Abel map via tropical geometry / Bertini’s t
heorem in positive characteristic\nby Sally Andria / César Hilário (
UFF / IMPA) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\
nAn explicit resolution of the Abel map via tropical geometry\, by Sally A
ndria (UFF)\n\nIn this talk I will talk about the problem studied in my th
esis: Is it possible to find an explicit resolution of the Abel map (a rat
ional map) for a nodal curve?\nWe start with a family of curves\, that is
a regular smoothing of a nodal curve with smooth components. We take a pol
arization\, an invertible sheaf\, and a section through the smooth locus o
f the family. The Abel map is the rational map taking a tuple of points $(
Q_1\,\\ldots\,Q_d)$ on a curve of the family to the associated sheaf in th
e Esteves compactified Jacobian. We translate this problem into an explici
t combinatorial problem by means of tropical and toric geometry. The solut
ion of the combinatorial problem gives rise to an explicit resolution of t
he Abel map.\n\n\n-- xx -- xx --\n\nBertini’s theorem in positive charac
teristic\, by Cesar Hilario (IMPA)\n\nA classical theorem of Bertini state
s that in characteristic zero almost all the fibers of a dominant morphism
between two smooth algebraic varieties are smooth\, that is\, there do no
t exist fibrations by singular varieties with smooth total space. Unfortun
ately\, Bertini’s theorem fails in positive characteristic\, as was firs
t observed by Zariski in the 1940s. Investigating such a failure naturally
leads to the classification of its exceptions. By a theorem of Tate\, a f
ibration by singular curves of arithmetic genus $g$ in characteristic $p >
0$ may exist only if $p \\le 2g + 1$. When $g = 1$ and $g = 2$\, these fi
brations have been studied by Queen\, Borges Neto\, Stohr and Simarra Cañ
ate. A birational classification of the case $g = 3$ was started by Stohr
($p = 7\, 5$)\, and then continued by Salomão ($p = 3$). In this talk I s
hall report on some progress in the case $g = 3$\, $p = 2$. In fact\, seve
ral examples show already that in this setting very interesting geometric
phenomena arise.\n
LOCATION:https://researchseminars.org/talk/BRAG/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damiano Testa (University of Warwick)
DTSTART;VALUE=DATE-TIME:20201007T183000Z
DTEND;VALUE=DATE-TIME:20201007T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/26
DESCRIPTION:Title: Co
ntact in algebraic and tropical geometry\nby Damiano Testa (University
of Warwick) as part of Brazilian algebraic geometry seminar\n\n\nAbstract
\nIn recent years\, classical enumerative problems in algebraic geometry h
ave been converted into statements in tropical geometry. This approach ha
s had tremendous success. In view of the current pandemic\, we will stay
away from these popular results. Rather\, we discuss two isolated cases:
the 9 inflection points of plane cubics and the 28 bitangent lines of plan
e quartics. The tropical counts yield 3 and 7\, respectively. We will se
e how to reconcile these results via positive characteristic. These cases
naturally generalize to inflection points of plane curves of arbitrary deg
ree and theta-characteristics of curves of general type.\n\nThe talk assum
es minimal familiarity with basic concepts of algebraic geometry over the
complex numbers. Positive characteristic and tropical geometry play import
ant\, but non-technical roles. This is joint work with Marco Pacini.\n\nLi
nk for the talk will be posted here a few days before the talk.\n
LOCATION:https://researchseminars.org/talk/BRAG/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Jardim (UNICAMP)
DTSTART;VALUE=DATE-TIME:20201014T183000Z
DTEND;VALUE=DATE-TIME:20201014T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/27
DESCRIPTION:Title: Cl
assification of codimension one distributions of degree two on the project
ive space\nby Marcos Jardim (UNICAMP) as part of Brazilian algebraic
geometry seminar\n\n\nAbstract\nIn this talk I will provide a complete cla
ssification of codimension one distributions of degree 2 on the three dim
ensional projective space\, generalizing the classification of codimensio
n one foliations of degree 2 given by Cerveau and Lins Neto. We describe a
ll possible singular schemes and tangent sheaves of such distributions and
speculate on the topological and algebraic properties of integrability.\n
LOCATION:https://researchseminars.org/talk/BRAG/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Douglas Guimarães (UNICAMP)
DTSTART;VALUE=DATE-TIME:20201028T183000Z
DTEND;VALUE=DATE-TIME:20201028T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/28
DESCRIPTION:Title: Mo
duli spaces of quasitrivial rank 2 sheaves\nby Douglas Guimarães (UNI
CAMP) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nDougl
as Guimarães (UNICAMP)\n\nTitle: Moduli spaces of quasitrivial rank 2 she
aves\n\nAbstract: A torsion free sheaf $E$ on $\\mathbb{P}^3$ is called qu
asitrivial if $E^{\\vee\\vee}=\\mathcal{O}_{\\mathbb{P}^3}^{\\oplus r}$ an
d $\\dim(E^{\\vee\\vee}/E)=0$. While such sheaves are always $\\mu$-semis
table\, they may not be Gieseker semistable. We study the moduli spaces of
$\\mu$- and Gieseker semistable quasitrivial sheaves of rank 2 via the q
uot scheme of points $Quot(\\mathcal{O}_{\\mathbb{P}^3}^{\\oplus 2}\,n)$\,
where $n=h^0(E^{\\vee\\vee}/E)$. We will show the construction of an irre
ducible component of the Gieseker moduli space which is birrational to the
total space of a $\\mathbb{P}^{n-1}$-bundle over $S(n-1)\\times\\mathbb{P
}^3$\, where $S(n)$ is the smoothable component of the Hilbert scheme of $
n$ points in $ \\mathbb{P}^3$. Furthermore\, this is the only irreducible
component when $n\\le10$.\n
LOCATION:https://researchseminars.org/talk/BRAG/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ageu Barbosa (UFPB)
DTSTART;VALUE=DATE-TIME:20201021T183000Z
DTEND;VALUE=DATE-TIME:20201021T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/29
DESCRIPTION:Title: On
$(h\,s)$-tangential weak defectiveness and identifiability of some projec
tive varieties\nby Ageu Barbosa (UFPB) as part of Brazilian algebraic
geometry seminar\n\n\nAbstract\nIn this talk\, I will present a new techni
que to study the problem of weak defectiveness using degenerations of tang
ent linear spaces to osculating linear spaces. I also will present a resul
t on tangential weak defectiveness for varieties admitting a fibration wit
h a linearly embedded $\\mathbb{P}^1$ as general fiber and apply it to obt
ain a sharp asymptotic bound for non secant defectiveness of Segre varieti
es.\n
LOCATION:https://researchseminars.org/talk/BRAG/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Israel Vainsencher (UFMG)
DTSTART;VALUE=DATE-TIME:20201104T183000Z
DTEND;VALUE=DATE-TIME:20201104T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/30
DESCRIPTION:Title: En
umerative geometry of legendrian foliations\nby Israel Vainsencher (UF
MG) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nFoliati
ons\, or more generally\, distributions\, provide a geometric\nviewpoint i
n the theory of differential equations. Grosso modo\,\na foliation of dime
nsion one\, is a (polynomial) recipe to draw a line\nat each point. We’l
l stick to 3-dim projective space. Similarly\, a\ndistribution of codimens
ion one assigns a plane at each point. We\nassume the coefficients of the
equation of the plane are of degree one.\nAs syzygies trained minds will r
ecognize\, this entails the distribution\nis specified by an anti-symmetri
c 4×4 matrix. Those of maximal\nrank correspond to the distributions of c
ontact. A foliation is called\nlegendrian whenever tangent to some distrib
ution of contact. Our\ngoal is to describe the calculation of the dimensio
n and degree of\nthe subvariety of legendrian foliations (and friends). It
turns out that\nthe answer is given by Athus polynomials. This fits into
a Schubert\nCalculus like programme of exploring the geometry of parameter
\nspaces of foliations.\n
LOCATION:https://researchseminars.org/talk/BRAG/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Kleiman (MIT)
DTSTART;VALUE=DATE-TIME:20210224T183000Z
DTEND;VALUE=DATE-TIME:20210224T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/31
DESCRIPTION:Title: Ge
ometry of Gorenstein Artinian Algebra\nby Steven Kleiman (MIT) as part
of Brazilian algebraic geometry seminar\n\n\nAbstract\nMacaulay Duality\,
between filtered quotients of a polynomial ring over\na field\, annihilat
ed by a power of the variables\, and Artinian\nsubmodules of the ring's gr
aded dual\, is generalized over any Noetherian\nground ring\, and used to
provide isomorphisms between the subschemes of\nthe Hilbert scheme paramet
erizing various sorts of these quotients\, and\nthe corresponding subschem
es of the Quot scheme of the dual. Notably\,\non this basis\, the scheme
of compressed Gorenstein algebras is proved to\nbe smooth and irreducible
of a certain relative dimension. Joint work in progress with Jan Kleppe.\n
LOCATION:https://researchseminars.org/talk/BRAG/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Gargiulo (IMPA)
DTSTART;VALUE=DATE-TIME:20201111T183000Z
DTEND;VALUE=DATE-TIME:20201111T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/32
DESCRIPTION:Title: Ra
tional pullbacks of toric foliations\nby Javier Gargiulo (IMPA) as par
t of Brazilian algebraic geometry seminar\n\n\nAbstract\nIn this talk we w
ill present a short digression about the theory of singular foliations on
toric varieties and certain algebraic spaces parametrizing them. In partic
ular\, we will construct families of singular foliations on a classical pr
ojective space that arise as pull-backs of foliations on a simplicial tori
c variety X under suitable rational maps. We will focus on the case wher
e X is a complete simplicial toric surface.\n\nThe singular set of a foli
ation is one of the most commonly studied geometric objects in the area. T
he geometry and topology near a singularity characterize (in some sense) t
he foliation. Not surprisingly\, most of the approaches to obtain stabilit
y results for singular foliations involve a detailed study of their singul
ar locus. In this respect\, we will attempt to describe certain aspects of
the singular and Kupka scheme of foliations on a toric surface and their
corresponding pull-backs. We will also characterize their first order unfo
ldings and deformations in some cases.\n
LOCATION:https://researchseminars.org/talk/BRAG/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Marchesi (Universitat de Barcelona)
DTSTART;VALUE=DATE-TIME:20201118T183000Z
DTEND;VALUE=DATE-TIME:20201118T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/33
DESCRIPTION:Title: Gr
oup actions on vector bundles\nby Simone Marchesi (Universitat de Barc
elona) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nThe
classification of vector bundles which are invariant under the action of a
determined group\, has been widely studied.\n\nWe can consider\, for exam
ple\, the canonical action of the projective linear group $PGL(n+1)$ on $\
\mathbb{P}^n$ which leads to the definition of homogeneous vector bundle.
The choice of specific subgroups has been often determined\, in literature
\, restricting our attention to particular families. Recall indeed that An
cona and Ottaviani proved that the Steiner bundles on $\\mathbb{P}^n$ that
are invariant under an action of $SL(2\,\\mathbb{C})$ are the so called S
chwarzenberger bundles. Another example\, moving into the realm of hyperpl
ane arrangements\, in which I have been particularly interested lately\, i
s given by the reflection arrangements. They are defined as hyperplane arr
angements that are invariant under the group generated by their reflection
s\, and it is known that their associated sheaf is free (a sum of line bun
dles) and therefore homogeneous.\n \nIn a previous work\, studying Nearly
-free arrangements\, we proved that their configuration of jumping lines i
s extremely special but remarked that it did not characterize this family
of arrangements. It turns out that they are characterized by the invarianc
e under the action of the subgroup $G_p \\subset \\mathrm{PGL}(3)$ that f
ixes the point $p$ in the projective plane. Inspired by this result\, we c
lassify vector bundles which are invariant under the action of subgroups t
hat fix linear subspaces of the projective plane.\n\nFinally\, we will foc
us on the relations between the geometry of the jumping locus and the inva
riance under the action of the group. Recall that\, historically\, such qu
estion has been studied in order to relate homogeneous bundles with unifor
m ones\, i.e. bundles for which the splitting type is constant.\n \nThis i
s the result of two collaborations: one with Jean Vallès and one with Ros
a Maria Miró-Roig.\n
LOCATION:https://researchseminars.org/talk/BRAG/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Lorscheid (IMPA)
DTSTART;VALUE=DATE-TIME:20201125T183000Z
DTEND;VALUE=DATE-TIME:20201125T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/34
DESCRIPTION:Title: Th
e moduli space of matroids\nby Oliver Lorscheid (IMPA) as part of Braz
ilian algebraic geometry seminar\n\n\nAbstract\nMatroids are combinatorial
gadgets that reflect properties of linear algebra in situations where thi
s latter theory is not available. This analogy prescribes that the moduli
space of matroids should be a Grassmannian over a suitable base object\, w
hich cannot be a field or a ring\; in consequence usual algebraic geometry
does not provide a suitable framework. In joint work with Matt Baker\, we
have used algebraic geometry over the so-called field with one element to
construct such moduli spaces. As an application\, we streamline various r
esults of matroid theory and find simplified proofs of classical theorems\
, such as the fact that a matroid is regular if and only if it is binary a
nd orientable.\n\nWe will dedicate the first part of this talk to an expos
ition of matroids. Then we will briefly outline how to construct the modul
i space of matroids. In a last part\, we will explain with some care why t
his theory is useful to simplify classical results in matroid theory.\n
LOCATION:https://researchseminars.org/talk/BRAG/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (IMPA)
DTSTART;VALUE=DATE-TIME:20201202T183000Z
DTEND;VALUE=DATE-TIME:20201202T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/35
DESCRIPTION:Title: Bi
rational geometry of Calabi-Yau pairs and 3-dimensional Cremona transforma
tions\nby Carolina Araujo (IMPA) as part of Brazilian algebraic geomet
ry seminar\n\n\nAbstract\nRecently\, Oguiso addressed the following questi
on\, attributed to Gizatullin: ``Which automorphisms of a smooth quartic K
3 surface $D\\subset \\PP^3$ are induced by Cremona transformations of the
ambient space $\\mathbb{P}^3$?'' \n\nWhen $D\\subset \\mathbb{P}^3$ is a
smooth quartic surface\, $(\\mathbb{P}^3\,D)$ is an example of a Calabi-Y
au pair\, that is\, a pair $(X\,D)$\, consisting of a normal projective va
riety $X$ and an effective Weil divisor $D$ on $X$ such that $K_X+D\\sim 0
$. Gizatullin's question is about birational properties of the Calabi-Yau
pair $(\\mathbb{P}^3\,D)$. In this talk\, I will explain a general framewo
rk to study the birational geometry of mildly singular Calabi-Yau pairs. T
hen I will focus on the case of singular quartic surfaces $D\\subset \\mat
hbb{P}^3$. Our results illustrate how the appearance of increasingly worse
singularities in $D$ enriches the birational geometry of the pair $(\\mat
hbb{P}^3\, D)$\, and lead to interesting subgroups of the Cremona group of
$\\mathbb{P}^3$.\n\nThis is joint work with Alessio Corti and Alex Massar
enti.\n
LOCATION:https://researchseminars.org/talk/BRAG/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian Martinez (UNICAMP)
DTSTART;VALUE=DATE-TIME:20210303T183000Z
DTEND;VALUE=DATE-TIME:20210303T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/36
DESCRIPTION:Title: St
ability under Fourier-Mukai transforms on elliptic surfaces\nby Cristi
an Martinez (UNICAMP) as part of Brazilian algebraic geometry seminar\n\n\
nAbstract\nLet $X$ be a Weierstrass elliptic surface. By moving the polari
zation towards the fiber direction while keeping the volume of the polariz
ation fixed\, we can define a notion of limit Bridgeland stability. In thi
s talk\, we will prove that under certain conditions the relative Fourier-
-Mukai transform of a slope semistable sheaf is a limit semistable object.
In the case that the surface has Picard rank two\, a detailed study of th
e potential Bridgeland walls will provide us with extra numerical conditio
ns to guarantee that the Fourier--Mukai transform of a 1-dimensional slope
semistable sheaf is Bridgeland semistable.\n\nZoom Meeting ID: 913 6913 4
478\n
LOCATION:https://researchseminars.org/talk/BRAG/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inder Kaur (PUC-Rio)
DTSTART;VALUE=DATE-TIME:20210310T183000Z
DTEND;VALUE=DATE-TIME:20210310T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/37
DESCRIPTION:Title: Qu
estions on the cohomology ring of moduli spaces of stable locally-free she
aves on curves\nby Inder Kaur (PUC-Rio) as part of Brazilian algebraic
geometry seminar\n\n\nAbstract\nLet $M(2\,L)$ denote the moduli space of
stable vector bundles of rank $2$ and determinant $L$ of odd degree\, on a
smooth curve of genus $g \\geq 2$. Owing to the work of Mumford\, Newstea
d\, Kirwan\, King and several others\, questions such as the generators an
d relations\, higher rank Torelli-type theorems as well as the Hodge conje
cture for the cohomology ring of $M(2\,L)$ are well understood. In this ta
lk I will survey some of these aspects for the smooth case and discuss ana
logous results for the case when the underlying curve is irreducible\, nod
al. This is joint work with Suratno Basu and Ananyo Dan.\n
LOCATION:https://researchseminars.org/talk/BRAG/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederico Quallbrunn (Universidad CAECE)
DTSTART;VALUE=DATE-TIME:20210317T183000Z
DTEND;VALUE=DATE-TIME:20210317T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/38
DESCRIPTION:Title: Un
foldings of Lie algebroids\nby Frederico Quallbrunn (Universidad CAECE
) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nWe will t
alk about the notion of unfolding\, first on\nfoliations\, and then genera
lizing this concept to the case of Lie\nalgebroids. We will show some resu
lts and examples appearing in a\njoint work with M.Corrêa and A.Molinuevo
.\n
LOCATION:https://researchseminars.org/talk/BRAG/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giosuè Muratore (UFMG)
DTSTART;VALUE=DATE-TIME:20210324T183000Z
DTEND;VALUE=DATE-TIME:20210324T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/39
DESCRIPTION:Title: En
umeration of rational contact curves via torus actions\nby Giosuè Mur
atore (UFMG) as part of Brazilian algebraic geometry seminar\n\n\nAbstract
\nComplex projective spaces of odd dimension have a unique contact structu
re. So\, in these spaces we have contact (Legendrian) rational curves. We
are interested in enumeration of such curves. We prove that some Gromov-Wi
tten numbers associated to rational contact curves in projective space wit
h arbitrary incidence conditions are enumerative. Also\, we use Bott formu
la on the Kontsevich space to find the exact value of those numbers.\n
LOCATION:https://researchseminars.org/talk/BRAG/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danny Taboada / Victor Pretti (UFF / UNICAMP)
DTSTART;VALUE=DATE-TIME:20210331T183000Z
DTEND;VALUE=DATE-TIME:20210331T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/40
DESCRIPTION:Title: Th
e moduli space of quasistable spin curves / Rank 0 Asymptotic Bridgeland s
tability\nby Danny Taboada / Victor Pretti (UFF / UNICAMP) as part of
Brazilian algebraic geometry seminar\n\n\nAbstract\nYoung BRAG\n\nSpeaker
1: Danny Taboada (UFF)\n\nTitle: The moduli space of quasistable spin curv
es\nAbstract: We study a compactification of the moduli space of theta cha
racteristics\, giving a modular interpretation of the geometric points and
describing the boundary stratification. This space is different from the
moduli space of spin curves. The modular description and the boundary stra
tification of the new compactification are encoded by a tropical moduli sp
ace. We show that this tropical moduli space is a refinement of the moduli
space of spin tropical curves. We describe explicitly the induced decompo
sition of its cones. This is a joint work with Abreu and Pacini.\n\n--XX--
XX--\n\nSpeaker 2: Victor Pretti (UNICAMP)\n\nTitle: Rank 0 Asymptotic Bri
dgeland stability\n\nAbstract: Bridgeland stability is a modern tool to st
udy stability of objetcs in triangulated categories\, and specially in the
derived category of coherent sheaves over a smooth projective variety. It
s asymptotic version\, as studied by Bridgeland\, Bayer and Jardim--Macioc
ia\, is known to behave like Gieseker stability for sheaves in various sit
uations. In this seminar we will focus on Bridgeland stabilities over the
projective space P^3 and its asymptotic behaviour for rank zero objects to
prove their respective relation with Gieseker stability for sheaves.\n\nT
wo 30 min presentations by PhD students or recently graduated PhDs.\n
LOCATION:https://researchseminars.org/talk/BRAG/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cancelled
DTSTART;VALUE=DATE-TIME:20210407T183000Z
DTEND;VALUE=DATE-TIME:20210407T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/41
DESCRIPTION:by Cancelled as part of Brazilian algebraic geometry seminar\n
\n\nAbstract\nWith great sadness\, we cancel the BRAG seminar today (07 Ap
ril 2021) due to the passing of our dear friend and colleague Roberto Call
ejas Bedregal\, last night by covid. May he always be remembered for his j
oy\, generosity and good heart\, and may he rest in peace.\n
LOCATION:https://researchseminars.org/talk/BRAG/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aline Andrade (UFF)
DTSTART;VALUE=DATE-TIME:20210414T183000Z
DTEND;VALUE=DATE-TIME:20210414T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/42
DESCRIPTION:Title: On
rank 3 instanton bundles on projective 3 space\nby Aline Andrade (UFF
) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nWe invest
igate rank $3$ instanton bundles on $\\mathbb{P}^3$ of charge $n$ and its
correspondence with rational curves of degree $n+3$. in order to prove tha
t the generic stable rank 3 ’t Hooft bundle of charge n is a smooth poin
t in the moduli space of rank 3 vector bundles of Chern classes (0\,n\,0).
Additionally\, for $n=2$ we present a correspondence between stable rank
$3$ instanton bundles and stable rank $2$ reflexive linear sheaves and we
prove that the moduli space of rank $3$ stable locally free sheaves on $\\
mathbb{P}^3$ of Chern classes $(0\,2\,0)$ is irreducible\, generically smo
oth of dimension 16. (Joint work with D. R. Santiago\, D. D. Silva\, and L
. S. Sobral)\n
LOCATION:https://researchseminars.org/talk/BRAG/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Ribon (UFF)
DTSTART;VALUE=DATE-TIME:20210505T183000Z
DTEND;VALUE=DATE-TIME:20210505T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/43
DESCRIPTION:Title: Lo
cal foliations with closed leaves\nby Javier Ribon (UFF) as part of Br
azilian algebraic geometry seminar\n\n\nAbstract\nOur goal is describing t
he leaf space of local holomorphic foliation whose leaves are closed in a
neighborhood of the origin. By considering the holonomy groups associated
to leaves\, it is necessary to study the finitely generated groups of loca
l biholomorphisms whose orbits are closed (or equivalently finite) in some
neighborhood of the origin. We show that for such groups\, there is alway
s an analytic curve through the origin that is contained in the fixed poin
t set of a finite index subgroup. Moreover\, we outline the properties of
the linear part of a local diffeomorphism with finite orbits. The result p
rovides a stability result à la Reeb in intermediate dimension for dimens
ion one foliations defined in the neighborhood of a compact invariant curv
e. This is a joint work with Lucivanio Lisboa and some of the results are
part of his PhD thesis.\n
LOCATION:https://researchseminars.org/talk/BRAG/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elizaveta Vishnyakova (UFMG)
DTSTART;VALUE=DATE-TIME:20210512T183000Z
DTEND;VALUE=DATE-TIME:20210512T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/44
DESCRIPTION:Title: Do
nagi-Witten construction and a graded covering of a supermanifold\nby
Elizaveta Vishnyakova (UFMG) as part of Brazilian algebraic geometry semin
ar\n\n\nAbstract\nIn the paper "Super Atiyah classes and obstructions to s
plitting of\nsupermoduli space"\, Donagi and Witten suggested a constructi
on of a\nfirst obstruction class for splitting of a supermanifold via\ndi
fferential operators. We generalize this idea. As a result we\nobtain a f
amily of embeddings of the category of supermanifolds into\nthe category o
f iterated vector bundles and into the category of\ngraded manifolds. It
was shown that the images of a supermanifold in\nthese categories satisfy
universal properties of a graded covering or\na graded semicovering. In ou
r talk we will discuss these functors in the case of a Lie supergroup and
a Lie superalgebra. (Joint work with M. Rotkiewicz).\n
LOCATION:https://researchseminars.org/talk/BRAG/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Paulo Figueiredo (IMPA)
DTSTART;VALUE=DATE-TIME:20210428T183000Z
DTEND;VALUE=DATE-TIME:20210428T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/45
DESCRIPTION:Title: Re
gular foliations on rationally connected threefolds with nef anticanonical
bundle\nby João Paulo Figueiredo (IMPA) as part of Brazilian algebra
ic geometry seminar\n\n\nAbstract\nIn his classification of regular foliat
ions on surfaces\, Brunella showed that every regular foliations on a rati
onal surface is algebraically integrable\, with rational leaves. This lead
s to the conjecture\, due to Touzet\, that every regular foliation on a ra
tionally connected manifold is algebraically integrable with rationally co
nnected leaves. This conjecture was shown to be true by Druel for the case
of Fano manifolds. In this talk\, we will present progress towards this c
onjecture for threefolds\, by showing that it is true for regular foliatio
ns of codimension one on threefolds with nef anticanonical bundle.\n
LOCATION:https://researchseminars.org/talk/BRAG/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Franco (IST Lisboa)
DTSTART;VALUE=DATE-TIME:20210519T183000Z
DTEND;VALUE=DATE-TIME:20210519T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/46
DESCRIPTION:Title: De
formation theory for orthogonal and symplectic sheaves\nby Emilio Fran
co (IST Lisboa) as part of Brazilian algebraic geometry seminar\n\n\nAbstr
act\nModuli spaces of principal bundles usually carry interesting\ngeometr
ic structures\, being a powerful\, and often unique\, source of\nexamples
of varieties with prescribed properties and characteristics.\nNevertheless
\, these spaces might be non-compact whenever the base\n(smooth) scheme ha
s dimension higher than 1. Principal sheaves provide a\nnatural compactifi
cation of the moduli space of principal bundles for a\nconnected complex r
eductive structure group. Therefore\, moduli spaces of\nprincipal sheaves
are projective varieties equipped with an interesting\ngeometry\, at least
\, on a dense subset. In order to check whether or not\nthese properties e
xtend to the compactification\, we need a local\ndescription of the moduli
spaces\, precisely over the locus where the\nprincipal sheaves fail to be
principal bundles. Such description would\nnaturally derive from deformat
ion theory of principal sheaves\, which is\nstill missing at present date.
\n\nIn this talk we consider orthogonal and symplectic sheaves\, and show\
nthat the deformation and obstruction theory of these objects is\ncontroll
ed by a deformation complex naturally built out of our starting\northogona
l (resp. symplectic) sheaf.\n
LOCATION:https://researchseminars.org/talk/BRAG/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeriano Lanza (UFF)
DTSTART;VALUE=DATE-TIME:20210526T183000Z
DTEND;VALUE=DATE-TIME:20210526T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/47
DESCRIPTION:Title: Mo
duli of flags of sheaves: a quiver description\nby Valeriano Lanza (UF
F) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nIn [1]\,
the moduli spaces of framed flags of sheaves on P2 were described by mean
s of representations of the so-called enhanced ADHM quiver. We first revie
w those results\, with a recent refinement concerning the chamber structur
e in the space of stability parameters. We shall then discuss the obstruct
ion theory for these moduli spaces\, showing in general that they have a
perfect obstruction theory\, and providing for specific choices of invaria
nts a class of unobstructed points. Finally\, open problems and possible f
urther developments will be presented. This is a joint work with Rodrigo v
on Flach and Marcos Jardim. \n\n[1] R. A. von Flach and M. Jardim\, Moduli
spaces of framed flags of sheaves on the projective plane. Journal of Geo
metry and Physics 118 (2017)\, 138–168.\n
LOCATION:https://researchseminars.org/talk/BRAG/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Massarenti (U. Ferrara)
DTSTART;VALUE=DATE-TIME:20210421T183000Z
DTEND;VALUE=DATE-TIME:20210421T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/48
DESCRIPTION:Title: Co
mplete symplectic quadrics and Kontsevich moduli spaces of conics in Lagra
ngian Grassmannians\nby Alex Massarenti (U. Ferrara) as part of Brazil
ian algebraic geometry seminar\n\n\nAbstract\nGiven a reductive algebraic
group $G$ and a Borel subgroup $B$\, a spherical variety\nis a normal vari
ety admitting an action of $G$ with an open dense $B$-orbit. A special\ncl
ass of spherical varieties are the so-called wonderful varieties. These ar
e smooth\nspherical varieties for which we require $G$ to be semisimple an
d simply connected\nand the existence of an open $B$-orbit whose complemen
tary set is a simple normal\ncrossing divisor. We will construct the wonde
rful compactification of the space of\nsymmetric\, symplectic matrices on
which the symplectic group acts. Furthermore\,\nwe will compute the Picard
group of this compactification and we will study its\nbirational geometry
in low-dimensional cases. As an application\, we will recover the\nresult
s on the birational geometry of the Kontsevich spaces of conics in Grassma
nnians\ndue to I. Coskun and D. Chen\, and we will prove new results on th
e birational\ngeometry of the Kontsevich spaces of conics in Lagrangian Gr
assmannians.\nThis is a joint work with Elsa Corniani.\n
LOCATION:https://researchseminars.org/talk/BRAG/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Montoya (UNICAMP)
DTSTART;VALUE=DATE-TIME:20210602T183000Z
DTEND;VALUE=DATE-TIME:20210602T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/49
DESCRIPTION:Title: An
extension of the Noether-Lefschetz loci in toric varieties\nby Willia
m Montoya (UNICAMP) as part of Brazilian algebraic geometry seminar\n\n\nA
bstract\nIn this talk\, I will motivate and prove a Noether-Lefschetz type
theorem for quasi-smooth intersections in a projective simplicial toric v
ariety with suitable conditions\, which implies that the Hodge conjecture
holds on a very general quasi-smooth intersection variety and that the nat
ural extension of the Noether-Lefchetz loci is not empty. The Noether-Lefs
chetz loci can be understood as the loci where the Hodge conjecture is unk
nown. If time allows me\, I will also show that the Hodge conjecture is al
so true for some varieties in the Noether-Lefschetz loci. This is joint wo
rk with Prof. Ugo Bruzzo.\n
LOCATION:https://researchseminars.org/talk/BRAG/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abramo Hefez\, Steven Kleiman\, Michelle Morgado\, Marcelo Saia\,
José Seade\, Otoniel Nogueira da Silva
DTSTART;VALUE=DATE-TIME:20210609T183000Z
DTEND;VALUE=DATE-TIME:20210609T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/50
DESCRIPTION:Title: An
afternoon of algebraic geometry in memory of Roberto Bedregal\nby Abr
amo Hefez\, Steven Kleiman\, Michelle Morgado\, Marcelo Saia\, José Seade
\, Otoniel Nogueira da Silva as part of Brazilian algebraic geometry semin
ar\n\n\nAbstract\nwe convene for a special edition of the BRAG (Brazilian
Algebraic Geometry Seminar) session in honor of our friend and colleague R
oberto Callejas-Bedregal\, who passed away on 6 April of this year. We wil
l have 15 minute lectures given by Abramo Hefez (UFF)\, Steven Kleiman (MI
T)\, Michelle Morgado (Unesp)\, Marcelo José Saia (UFSCar)\, José Seade
(UNAM) and Otoniel Nogueira da Silva (UNAM)\, along with testimonials from
Roberto's students\, friends and colleagues.\n\n-- xx -- xx --\n\n1 - Abr
amo Hefez: The mathematical trajectory of Roberto Bedregal Abstract:\nThe
aim of this short talk is to sketch Bedregal's journey towards his mathema
tical achievements.\n\n\n-- xx -- xx --\n\n2 - Steve Kleiman: Roberto's MI
T Thesis\nTo begin\, some introductory remarks are made about how Roberto\
ncame to study at MIT and to develop the first purely algebraic treatment\
nof the Whitney Conditions. Then the main result of his thesis is\nstated
\, and its terms\, explained. Finally\, an inkling is given of the\nimpor
t of the Whitney Conditions.\n\n-- xx -- xx --\n\n3 - José Seade: Chern c
lasses for singular varieties.\nI will speak about some of the joint work
I did recently with Roberto Callejas-Bedregal and Michelle Morgado\, about
Chern classes of singular varieties.\n\n-- xx -- xx --\n\n4 - Michelle Mo
rgado: Lê cycles\n\n-- xx -- xx --\n\n5 - Marcelo José Saia: On Segre nu
mbers of homogeneous map germs\n\n-- xx -- xx --\n\n6 - Otoniel Nogueira d
a Silva: Equisingularity of families of map germs and Ruas's Conjecture\n\
n-- xx -- xx --\n\n7 - Presentation of a video made by Roberto's students.
\n
LOCATION:https://researchseminars.org/talk/BRAG/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaia Comaschi (University of Campinas)
DTSTART;VALUE=DATE-TIME:20210616T183000Z
DTEND;VALUE=DATE-TIME:20210616T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/51
DESCRIPTION:Title: In
stanton sheaves of low charge on Fano threefolds\nby Gaia Comaschi (Un
iversity of Campinas) as part of Brazilian algebraic geometry seminar\n\n\
nAbstract\nLet $X$ be a Fano threefold of Picard number one and of index $
2+h\, \\ h=0\,1$. \nAn \\textit{instanton sheaf of charge $k$ on $X$} is d
efined as a semi-stable rank 2 torsion free sheaf $F$ with Chern classes $
c_1=-h\, \\ c_2=k\, \\ c_3=0$ and such that $F(-1)$ has no cohomology.\nLo
cally free instantons\, originally defined on the projective space and lat
er generalised on other Fano threefolds $X$\, had been largely studied fro
m several authors in the past years\; their moduli spaces present an extre
mely rich geometry and useful applications to the study of curves on $X$.\
nIn this talk I will illustrate several features of non-locally free insta
ntons of low charge on 3 dimensional quadrics and cubics. I will focus in
particular on the role that they play in the study of the Gieseker-Maruyam
a moduli space $M_X(2\;-h\,k\,0)$ and describe how we can still relate the
se sheaves to curves on $X$.\n
LOCATION:https://researchseminars.org/talk/BRAG/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Jardim (University of Campinas)
DTSTART;VALUE=DATE-TIME:20210623T183000Z
DTEND;VALUE=DATE-TIME:20210623T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/52
DESCRIPTION:Title: Lo
garithmic sheaves for complete intersections\nby Marcos Jardim (Univer
sity of Campinas) as part of Brazilian algebraic geometry seminar\n\nAbstr
act: TBA\n
LOCATION:https://researchseminars.org/talk/BRAG/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Letterio Gatto (Politecnico di Torino)
DTSTART;VALUE=DATE-TIME:20210630T183000Z
DTEND;VALUE=DATE-TIME:20210630T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/53
DESCRIPTION:Title: On
the Vertex Operators Representation of Lie Algebras of Matrices\nby L
etterio Gatto (Politecnico di Torino) as part of Brazilian algebraic geome
try seminar\n\n\nAbstract\nRelying on our common skill to multiply square
matrices by vectors\, recalled in the first part of the talk\, we will des
cribe the exterior algebra of a polynomial ring in one indeterminate\, and
/or the ring of symmetric polynomials\, as a representation of the Lie alg
ebra of matrices of infinite size with all but finitely many zero entries.
\n\nThe description is achieved by bridging classical Schubert calculus on
Grassmannians to the vertex operators occurring in the so-called boson-fe
rmion correspondence (Poincaré duality for Grassmannians of infinite dime
nsional linear spaces) and highlights a substantial generalization of a cl
assical picture drawn in the Eighties by Date\, Jimbo\, Kashiwara and Miwa
\, within the framework of algebraic analysis and infinite dimensional com
pletely integrable systems. The talk will survey joint work with (in alpha
betical order) O. Behzad\, A. Contiero\, D. Martins\, P. Salehyan\, I. Sch
erbak and R. Vidal Martins.\n
LOCATION:https://researchseminars.org/talk/BRAG/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arturo Fernández Pérez (Federal University of Minas Gerais (UFMG
))
DTSTART;VALUE=DATE-TIME:20210825T183000Z
DTEND;VALUE=DATE-TIME:20210825T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/55
DESCRIPTION:Title: Nu
mber of Milnor and Tjurina of Foliations\nby Arturo Fernández Pérez
(Federal University of Minas Gerais (UFMG)) as part of Brazilian algebraic
geometry seminar\n\n\nAbstract\nIn this talk\, I will show the relationsh
ip between the Milnor and Tjurina numbers of a foliation in the complex pl
ane. Such numbers are similar to the classic Milnor and Tjurina numbers fo
r singular curves. This work is in collaboration with Evelia García Barro
so (Universidad de la Laguna - Spain) and Nancy Saravia Molina (PUCP-Peru)
\n
LOCATION:https://researchseminars.org/talk/BRAG/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thiago Fassarella (UFF)
DTSTART;VALUE=DATE-TIME:20210901T183000Z
DTEND;VALUE=DATE-TIME:20210901T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/56
DESCRIPTION:Title: Mo
duli spaces of parabolic Higgs bundles\nby Thiago Fassarella (UFF) as
part of Brazilian algebraic geometry seminar\n\n\nAbstract\nWe are interes
ted in studying moduli spaces of parabolic Higgs bundles on (punctured) cu
rves. A ramified cover between curves defines a map between the correspond
ing moduli spaces\, and we will discuss the behavior of this map with resp
ect to the Hitchin fibration. This is joint work in progress with Frank L
oray.\n
LOCATION:https://researchseminars.org/talk/BRAG/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hossein Movasati (IMPA)
DTSTART;VALUE=DATE-TIME:20210908T183000Z
DTEND;VALUE=DATE-TIME:20210908T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/57
DESCRIPTION:Title: Ib
iporanga: A moduli space for differential equations of automorphic forms\nby Hossein Movasati (IMPA) as part of Brazilian algebraic geometry sem
inar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BRAG/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rodrigo Salomão (UFF)
DTSTART;VALUE=DATE-TIME:20210915T183000Z
DTEND;VALUE=DATE-TIME:20210915T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/58
DESCRIPTION:Title: On
the classification of fibrations by singular curves on unirational surfac
es\nby Rodrigo Salomão (UFF) as part of Brazilian algebraic geometry
seminar\n\n\nAbstract\nIn 1944 Zariski discovered that Bertini’s theorem
on variable singular points is no longer true when we pass from a field o
f characteristic zero to a field of positive characteristic. In other word
s\, he found fibrations by singular curves\, which only exist in positive
characteristic. Such fibrations are connected with many interesting phenom
ena. For instance\, the extension of Enrique’s classification of surface
s to positive characteristic (Bombieri and Mumford in 1976)\, the countere
xamples of Kodaira vanishing theorem (Mukai in 2013 and Zheng in 2016) and
the isolated singularities with infinity Milnor number (jointly work with
Hefez and Rodrigues in 2019). In this talk we are going to show that the
smoothing process introduced by Shimada in 1991 can be used to describe th
e set of fibrations by genus two singular curves on unirational surfaces\,
up to isomorphism among their generic fibers\, such that the smoothing ar
e elliptic fibrations. Moreover we will also describe the vector fields wh
ose tangencies with elliptic fibrations generate such fibrations by singul
ar curves\, after the quotient of the rational elliptic surfaces. This is
a work in progress with J. H. O. Rodrigues and R. O. C. Santos.\n
LOCATION:https://researchseminars.org/talk/BRAG/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ommolbanin Behzad / Eduardo Vital (University of Isfahan\, Iran /
IMPA\, Brazil)
DTSTART;VALUE=DATE-TIME:20210929T183000Z
DTEND;VALUE=DATE-TIME:20210929T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/59
DESCRIPTION:Title: Ex
terior powers\, Polynomial rings and Representation of Lie Algebras / Dege
nerations of linear series to curves with three components\, using quiver
representations\nby Ommolbanin Behzad / Eduardo Vital (University of I
sfahan\, Iran / IMPA\, Brazil) as part of Brazilian algebraic geometry sem
inar\n\n\nAbstract\nYoung BRAG with two short presentations:\n\nSpeaker 1:
Ommolbanin Behzad (University of Isfahan\, Iran)\n\nTitle: Exterior power
s\, Polynomial rings and Representation of Lie Algebras\n\nAbstract: I wil
l report on some recent work of myself\, A. Contiero\, D.\nMartins\, R. Vi
dal Martins about representing lie algebras of vector space\nendomorphisms
on exterior algebras\, seeing it as the finite type case of the\ncelebrat
ed DJKM bosonic vertex operator representation of gl∞(Q).\n\n\n-- xx --
xx --\n\n\nSpeaker 2: Eduardo Vital (IMPA\, Brazil)\n\nTitle: Degeneration
s of linear series to curves with three components\, using quiver represen
tations\n\nAbstract: We explore the existence of simple bases for certain
special quiver representations arising from degenerations of linear series
on nodal curves. The existence\nof a simple basis implies that the repres
entation decomposes into representations\nof dimension one and simplifies
the calculus of the Hilbert polynomial of the\nquiver Grassmannian associa
ted to the representation. For these quiver representations\, we character
ise the existence of a simple basis with a local condition.\nAnd to a noda
l curve with three components we show that its linked projective\nspace is
Cohen-Macaulay\, reduced\, and has pure dimension.\nThis is a joint work
in progress with Eduardo Esteves and Renan Santos.\n
LOCATION:https://researchseminars.org/talk/BRAG/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Vallès (University of Pau\, France)
DTSTART;VALUE=DATE-TIME:20211006T183000Z
DTEND;VALUE=DATE-TIME:20211006T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/60
DESCRIPTION:Title: Fr
ee curves obtained from a pencil of algebraic curves\nby Jean Vallès
(University of Pau\, France) as part of Brazilian algebraic geometry semin
ar\n\n\nAbstract\nAn algebraic curve of the projective plane is free if it
s module of tangent vectors fields is free\,\nin other words\, if it is ge
nerated globally by two tangent vector fields.\nBeing given two algebraic
curves without common component I propose a new method to produce free cur
ves\n and a theorem explaining why they are free.\n
LOCATION:https://researchseminars.org/talk/BRAG/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacqueline Arancibia (UFPB)
DTSTART;VALUE=DATE-TIME:20211027T183000Z
DTEND;VALUE=DATE-TIME:20211027T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/61
DESCRIPTION:Title: So
me applications of Bott's Localization Formula in Enumerative Problems
\nby Jacqueline Arancibia (UFPB) as part of Brazilian algebraic geometry s
eminar\n\n\nAbstract\nFirst of all we explain what are the mathematical ob
jects involved in the Bott's localization formula. Next\, we apply the Bot
t's localization formula to resolve the classical problem of four lines (f
rom Schubert's Calculus)\, as well as\, to compute the degree of the subv
ariety formed by the surfaces of degree d in ${\\mathbb P}^3$ containing
a conic and two points varying on a fixed line.\n
LOCATION:https://researchseminars.org/talk/BRAG/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cleto B. Miranda-Neto (UFPB)
DTSTART;VALUE=DATE-TIME:20211103T183000Z
DTEND;VALUE=DATE-TIME:20211103T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/62
DESCRIPTION:Title: Va
nishing of Ext modules and characterizations of smoothness in algebraic va
rieties\nby Cleto B. Miranda-Neto (UFPB) as part of Brazilian algebrai
c geometry seminar\n\n\nAbstract\nIn this talk\, after presenting some hom
ological results which establish freeness criteria for modules\, I will di
scuss how the vanishing of suitable Ext modules can be translated in terms
of smoothness of a complex algebraic variety at a given point. Special at
tention will be given\, e.g.\, to complete intersections and rational surf
ace singularities.\n
LOCATION:https://researchseminars.org/talk/BRAG/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Hassanzadeh (UFRJ)
DTSTART;VALUE=DATE-TIME:20211110T183000Z
DTEND;VALUE=DATE-TIME:20211110T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/63
DESCRIPTION:Title: A
genus explanation of Buchsbaum-Rim multiplicity\nby Hamid Hassanzadeh
(UFRJ) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\nWe e
xplain the Buchsbaum-Rim multiplicity as the Euler-Poincare characteristic
of an “ordinary” Koszul complex. This provides a generalization of Se
rre’s formula for the Hilbert-Samuel multiplicity in terms of the length
of the Koszul homologies.The talk is based on a joint work with: Viniçiu
s Bouça\, Thiago Fiel and Jose Naeliton.\n
LOCATION:https://researchseminars.org/talk/BRAG/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristhian Garay (CIMAT\, Guanajuato)
DTSTART;VALUE=DATE-TIME:20211117T183000Z
DTEND;VALUE=DATE-TIME:20211117T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/64
DESCRIPTION:Title: In
flection polynomials of linear series on superelliptic curves\nby Cris
thian Garay (CIMAT\, Guanajuato) as part of Brazilian algebraic geometry s
eminar\n\n\nAbstract\nWe explore the inflectionary behavior of linear seri
es on families of marked superelliptic curves (i.e.\, cyclic covers of P^1
). The inflection of these linear series supported away from the superelli
ptic ramification locus is parameterized by the inflection polynomials\, a
certain infinite class of polynomials generalizing the division polynomia
ls (which are used to compute the torsion points of elliptic curves).\n\nT
hese polynomials are remarkable since their properties reflect aspects of
the underlying family of superelliptic curves. We also obtain inflectionar
y varieties\, which describe the global behaviour of the inflection points
on the family.\n\nIn this talk we will introduce these inflection polynom
ials and some of their properties. We report on joint work with Ethan Cot
terill\, Ignacio Darago\, Changho Han\, and Tony Shaska.\n
LOCATION:https://researchseminars.org/talk/BRAG/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margarida Melo (Roma Tre University)
DTSTART;VALUE=DATE-TIME:20211124T183000Z
DTEND;VALUE=DATE-TIME:20211124T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/65
DESCRIPTION:Title: Tr
opicalization of the universal Jacobian: logarithmic and non-archimedean v
iewpoints\nby Margarida Melo (Roma Tre University) as part of Brazilia
n algebraic geometry seminar\n\n\nAbstract\nWe construct a tropical univer
sal Jacobian on the category of cone stacks\, generalizing previous work b
y Abreu and Pacini. We then show that this cone stack can be obtained by t
ropicalizing two versions of the algebraic universal Jacobian: the logarit
hmic universal Jacobian and the non-archimedean universal Jacobian. We the
n discuss the connection between our construction and Molcho-Wise’s loga
rithmic Picard and Picard stacks. The talk will be based on joint work wit
h S. Molcho\, M. Ulirsch\, F. Viviani and J. Wise.\n\nhttps://impa-br.zoom
.us/j/86824790044?pwd=aDBhcXRVWjR5RXdUeHRhVFdVMzVYUT09\n
LOCATION:https://researchseminars.org/talk/BRAG/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Esteves (IMPA)
DTSTART;VALUE=DATE-TIME:20211201T183000Z
DTEND;VALUE=DATE-TIME:20211201T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/66
DESCRIPTION:Title: De
generations of line bundles and divisors along curves\nby Eduardo Este
ves (IMPA) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\n
A family of line bundles along a family of smooth curves parameterized by
the\npunctured disk can be extended in several ways over the limit stable
curve of the\nfamily. On the other hand\, the associated divisors can each
be extended in a unique way. We will discuss the interplay between these
two dynamics\, part of an ongoing work to address the problem raised by Ei
senbud and Harris in the 1980’s of constructing a useful moduli of limit
linear series over the\nmoduli of stable curves. It involves collaboratio
n with Piere Rodríguez\, Renan Santos\, Eduardo Vital (IMPA) and Omid Ami
ni (École Polytechnique).\n
LOCATION:https://researchseminars.org/talk/BRAG/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renato Vidal Martins (UFMG)
DTSTART;VALUE=DATE-TIME:20211208T183000Z
DTEND;VALUE=DATE-TIME:20211208T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/67
DESCRIPTION:Title: Th
e Gonality of an Integral Curve\nby Renato Vidal Martins (UFMG) as par
t of Brazilian algebraic geometry seminar\n\n\nAbstract\nThis talk introdu
ces gonality for arbitrary integral curves\, and reports\non joint work in
progress with Steve Kleiman. Discussed are topics that\nappear naturally
\, including the following: linear series defined by\ntorsion-free sheaves
of rank 1\; the relation among gonality\, scrolls\,\nand canonical models
\; and an upper bound on gonality.\n
LOCATION:https://researchseminars.org/talk/BRAG/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (Impa)
DTSTART;VALUE=DATE-TIME:20230426T173000Z
DTEND;VALUE=DATE-TIME:20230426T183000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/68
DESCRIPTION:Title: Th
e Calabi Problem for Fano Threefolds\nby Carolina Araujo (Impa) as par
t of Brazilian algebraic geometry seminar\n\n\nAbstract\nThe Calabi Proble
m is a formidable problem in the confluence of differential and algebraic
geometry. It asks which compact complex manifolds admit a Kähler-Einstein
metric. A necessary condition for the existence of such a metric is that
the canonical class of the manifold has a definite sign. For manifolds wit
h zero or positive canonical class\, the Calabi problem was solved by Yau
and Aubin/Yau in the 1970s. They confirmed Calabi's prediction\, showing t
hat these manifolds always admit a Kähler-Einstein metric. On the other h
and\, for projective manifolds with negative canonical class\, called “F
ano manifolds”\, the problem is much more subtle: Fano manifolds may or
may not admit a Kähler-Einstein metric. The Calabi problem for Fano manif
olds has attracted much attention in the last decades\, resulting in the f
amous Yau-Tian-Donaldson conjecture. The conjecture\, which is now a theor
em\, states that a Fano manifold admits a Kähler-Einstein metric if and o
nly if it satisfies a sophisticated algebro-geometric condition\, called
“K-polystability”. In the last few years\, tools from birational geome
try have been used with great success to investigate K-polystability. In t
his talk\, I will present an overview of the Calabi problem\, the recent c
onnections with birational geometry\, and the current state of the art in
dimension 3.\n
LOCATION:https://researchseminars.org/talk/BRAG/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thiago Fassarella (UFF)
DTSTART;VALUE=DATE-TIME:20230426T190000Z
DTEND;VALUE=DATE-TIME:20230426T200000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/69
DESCRIPTION:Title: To
relli-type theorems\nby Thiago Fassarella (UFF) as part of Brazilian a
lgebraic geometry seminar\n\n\nAbstract\nIn this talk\, I will present som
e Torelli-type theorems concerning moduli spaces of parabolic vector bundl
es and logarithmic connections over an elliptic curve. In the case of vect
or bundles\, we extend a classical theorem of D. Mumford and P. Newstead t
o the parabolic context (joint work with Luana Justo). For connections\, w
e recover the spectral data from the symplectic structure of the moduli sp
ace (joint work with Frank Loray and Alan Muniz).\n
LOCATION:https://researchseminars.org/talk/BRAG/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Israel Vainsencher (UFMG)
DTSTART;VALUE=DATE-TIME:20230629T140000Z
DTEND;VALUE=DATE-TIME:20230629T145000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/70
DESCRIPTION:Title: Gr
au de componentes do espaço de folheações em P^3\nby Israel Vainsen
cher (UFMG) as part of Brazilian algebraic geometry seminar\n\n\nAbstract\
nRevisitaremos algumas componentes conhecidas\, e.g.\,\n1) $\\{aA dB-bB dA
\, a=\\deg A/mdc\, b=\\deg B/mdc\\}$\; \n2) pullback linear $\\mathbb{P}^3
\\rightarrow \\mathbb{P}^2$\;\n3) pullback linear $\\mathbb{P}^3 \\righta
rrow \\mathbb{P}^1 \\times \\mathbb{P}^1$.\nO primeiro caso tem grau conhe
cido apenas se $a|b$ ou se $a=2$ e $b$ é ímpar. O segundo caso admite um
a fórmula explícita. Por fim\, explicaremos trabalho em andamento com Vi
vi Ferrer sobre o grau de componentes descobertas recentemente por Wodson
Mendson.\n
LOCATION:https://researchseminars.org/talk/BRAG/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mauricio Corrêa (U. Bari)
DTSTART;VALUE=DATE-TIME:20230629T150000Z
DTEND;VALUE=DATE-TIME:20230629T155000Z
DTSTAMP;VALUE=DATE-TIME:20230925T223712Z
UID:BRAG/71
DESCRIPTION:Title: En
umerative geometry of Legendrian foliations: a tale of contact\nby Mau
ricio Corrêa (U. Bari) as part of Brazilian algebraic geometry seminar\n\
n\nAbstract\nA foliation by curves is called Legendrian if it is tangent t
o some distribution of contact on a projective 3-space. Our goal is to giv
e formulas for the dimensions and degrees of the varieties of Legendrian f
oliations\, and of the varieties of foliations tangent to a pencil of plan
es which are in terms of Athus polynomial. This is a joint work with Israe
l Vainsencher.\n
LOCATION:https://researchseminars.org/talk/BRAG/71/
END:VEVENT
END:VCALENDAR