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BEGIN:VEVENT
SUMMARY:Ugo Bruzzo (SISSA / UFPB)
DTSTART:20210208T130000Z
DTEND:20210208T140000Z
DTSTAMP:20260422T212858Z
UID:Bandoleros-2021/1
DESCRIPTION:Title: Semistable Higgs bundles on elliptic surfaces\nby Ugo Bruzzo (
SISSA / UFPB) as part of V Algebraic Geometry Summer Meeting - Bandoleros
2021\n\n\nAbstract\nWe analyze Higgs bundles $(V\,\\phi)$ on a class of el
liptic surfaces $\\pi:X\\to B$\, whose underlying vector bundle $V$ has ve
rtical determinant and is fiberwise semistable. We prove that if the spect
ral curve of $V$ is reduced\, then the Higgs field $\\phi$ is vertical\, w
hile if the bundle $V$ is fiberwise regular with reduced (resp.\, integral
) spectral curve\, and if its rank and second Chern number satisfy an ineq
uality involving the genus of $B$ and the degree of the fundamental line b
undle of $\\pi$ (resp.\, if the fundamental line bundle is sufficiently am
ple)\, then $\\phi$ is scalar. We apply these results to the problem of ch
aracterizing slope-semistable Higgs bundles with vanishing discriminant on
the class of elliptic surfaces considered\, in terms of the semistability
of their pull-backs via maps from arbitrary (smooth\, irreducible\, compl
ete) curves to $X$. Work in collaboration with V. Peragine.\n
LOCATION:https://researchseminars.org/talk/Bandoleros-2021/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuqiang Qin (UNC)
DTSTART:20210208T141500Z
DTEND:20210208T151500Z
DTSTAMP:20260422T212858Z
UID:Bandoleros-2021/2
DESCRIPTION:Title: Compactification of the moduli space of minimal instantons on the
Fano threefold $V_4$\nby Xuqiang Qin (UNC) as part of V Algebraic Geom
etry Summer Meeting - Bandoleros 2021\n\n\nAbstract\nInstanton bundles wer
e first introduced on $\\mathbb{P}^{3}$ as stable rank $2$ bundles E with
$c_1(E)=0$ and ${\\textrm H}^1(E(-2))=0.$ Torsion free generalizations and
properties of moduli spaces of instanton bundles have been widely studied
. Faenzi and Kuznetsov generalized the notion of instanton bundles to othe
r Fano threefolds. In this talk\, we look at semistable sheaves of rank 2
with Chern classes $c_1 = 0\,$ $c_2 = 2$ and $c_3 = 0$ on the Fano threefo
ld $V_4$ of Picard number $1\,$ degree $4$ and index $2.$ We show that the
moduli space of such sheaves is isomorphic to the moduli space of semista
ble rank $2\,$ degree $0$ vector bundles on a genus $2$ curve. This provid
es a smooth compactification of the moduli space of minimal instanton bund
les on $V_4.$\n
LOCATION:https://researchseminars.org/talk/Bandoleros-2021/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincenzo Antonelli (Politecnico di Torino)
DTSTART:20210208T153000Z
DTEND:20210208T173000Z
DTSTAMP:20260422T212858Z
UID:Bandoleros-2021/3
DESCRIPTION:Title: Ulrich bundles on Hirzebruch surfaces\nby Vincenzo Antonelli (
Politecnico di Torino) as part of V Algebraic Geometry Summer Meeting - Ba
ndoleros 2021\n\n\nAbstract\nUlrich bundles on a projective variety are ve
ctor bundles without intermediate cohomology and with the maximal possible
numbers of generators. They can be considered as the vector bundles with
the simplest possible cohomology. \\\\ In this talk we characterize Ulrich
bundles of any rank on polarized rational ruled surfaces over $\\mathbb{P
}^1$. We show that every Ulrich bundle admits a resolution in terms of lin
e bundles. Conversely\, given an injective map between suitable totally de
composed vector bundles\, we show that its cokernel is Ulrich if it satisf
ies a vanishing in cohomology. Then we deal with the admissible ranks and
first Chern classes of an Ulrich bundle and we present some results about
the moduli space of stable Ulrich bundles.\n
LOCATION:https://researchseminars.org/talk/Bandoleros-2021/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Faenzi (Université de Bourgogne)
DTSTART:20210210T130000Z
DTEND:20210210T140000Z
DTSTAMP:20260422T212858Z
UID:Bandoleros-2021/4
DESCRIPTION:Title: Ulrich bundles on cubic fourfolds\nby Daniele Faenzi (Universi
té de Bourgogne) as part of V Algebraic Geometry Summer Meeting - Bandole
ros 2021\n\n\nAbstract\nI will report on joint work with Yeongrak Kim. Ulr
ich bundles on an $n-$dimensional closed subscheme $X$ of $\\mathbb{P}^{N}
$ are defined as sheaves whose associated module of global sections has a
free linear resolution of $N-n$ steps. I will prove that any smooth cubic
fourfold $X$ carries an Ulrich sheaf of rank 6. This is the minimal possib
le rank of an Ulrich sheaf when the fourfold is very general.\n
LOCATION:https://researchseminars.org/talk/Bandoleros-2021/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianfranco Casnati (Politecnico di Torino)
DTSTART:20210210T141500Z
DTEND:20210210T151500Z
DTSTAMP:20260422T212858Z
UID:Bandoleros-2021/5
DESCRIPTION:Title: Ulrich bundles on some regular surfaces\nby Gianfranco Casnati
(Politecnico di Torino) as part of V Algebraic Geometry Summer Meeting -
Bandoleros 2021\n\n\nAbstract\nAn Ulrich bundle on a variety X inside the
projective N-space $\\mathbb{P}^{N}$ over the complex field is a vector bu
ndle that admits a linear minimal free resolution as a sheaf on $\\mathbb{
P}^{N}$. Ulrich bundles have many interesting properties. E.g. they are se
mistable and have no intermediate cohomology: moreover\, their existence o
n a hypersurface $X$ is related to the problem of expressing a power of th
e polynomial defining $X$ as a linear determinant. Ulrich bundles on compl
ex curves can be easily described. This is no longer true for Ulrich bundl
es on surfaces\, though an almost easy characterization is still possible.
In the talk we focus our attention on the latter case. In particular we s
tudy the case of surfaces $S$ with $q(S):=h^1(O_S)=0$ satisfying some furt
her technical restriction\, showing the existence of simple Ulrich bundle
s of rank 2 on them. We also deal with examples for all the admissible val
ues of the Kodaira dimension of $S$.\n
LOCATION:https://researchseminars.org/talk/Bandoleros-2021/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatemeh Rezaee (Loughborough University)
DTSTART:20210210T153000Z
DTEND:20210210T173000Z
DTSTAMP:20260422T212858Z
UID:Bandoleros-2021/6
DESCRIPTION:Title: Birational behaviour of sheaves on threefolds\nby Fatemeh Reza
ee (Loughborough University) as part of V Algebraic Geometry Summer Meetin
g - Bandoleros 2021\n\n\nAbstract\nI will describe a new wall-crossing phe
nomenon of sheaves on the projective 3-space that induces singularities wh
ich are not allowed in the sense of the Minimal Model Program. Therefore\,
it cannot be detected as an operation in the Minimal Model Program of the
moduli space\, unlike the case for many surfaces.\n
LOCATION:https://researchseminars.org/talk/Bandoleros-2021/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander S. Tikhomirov (Higher School of Economics\, Moscow)
DTSTART:20210212T130000Z
DTEND:20210212T140000Z
DTSTAMP:20260422T212858Z
UID:Bandoleros-2021/7
DESCRIPTION:Title: Construction of symplectic vector bundles on projective space $\\
mathbb{P}^3$\nby Alexander S. Tikhomirov (Higher School of Economics\,
Moscow) as part of V Algebraic Geometry Summer Meeting - Bandoleros 2021\
n\n\nAbstract\nThe moduli spaces of symplectic vector bundles of arbitrary
rank on projective space $\\mathbb{P}^3$ are far from being well-understo
od. By now the only type of such bundles having satisfactory description a
re the so-called tame symplectic instantons. It is shown by U. Bruzzo\, D.
Markushevich and the author in two papers from 2012 and 2016 that the mod
uli spaces of tame symplectic instantons are irreducible generically reduc
ed algebraic spaces of dimension prescribed by the deformation theory. In
the present paper we construct an infinite series of smooth irreducible mo
duli components of symplectic vector bundles of an arbitrary even rank $2r
\,r\\ge1$\, obtained by an iterative use of the monad construction applied
to tame symplectic instantons. As a particular case we obtain an infinite
series of irreducible moduli components of stable rank 2 vector bundles o
n $\\mathbb{P}^3$. We show that this series contains as a subseries a larg
e part of an infinite series of moduli components constructed by the autho
r\, S. Tikhomirov and D. Vassiliev in 2019. We also prove that\, for any i
ntegers $n\,r$\, where $r\\ge1$ and $n\\ge r+147$\, there exists a moduli
component\, not necessarily unique\, of our series such that symplectic bu
ndles from this component have rank $2r$ and second Chern class $n$.\n
LOCATION:https://researchseminars.org/talk/Bandoleros-2021/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aline V. Andrade (UFF)
DTSTART:20210212T141500Z
DTEND:20210212T151500Z
DTSTAMP:20260422T212858Z
UID:Bandoleros-2021/8
DESCRIPTION:Title: On rank 3 instanton bundles on projective 3 space\nby Aline V.
Andrade (UFF) as part of V Algebraic Geometry Summer Meeting - Bandoleros
2021\n\n\nAbstract\nWe investigate rank $3$ instanton bundles on $\\mathb
b{P}^3$ of charge $n$ and its correspondence with rational curves of degre
e $n+3$. in order to prove that the generic stable rank 3 ’t Hooft bundl
e of charge n is a smooth point in the moduli space of rank 3 vector bundl
es of Chern classes (0\,n\,0). Additionally\, for $n=2$ we present a corre
spondence between stable rank $3$ instanton bundles and stable rank $2$ re
flexive linear sheaves and we prove that the moduli space of rank $3$ stab
le locally free sheaves on $\\mathbb{P}^3$ of Chern classes $(0\,2\,0)$ is
irreducible\, generically smooth of dimension 16. (Joint work with D. R.
Santiago\, D. D. Silva\, and L. S. Sobral)\n
LOCATION:https://researchseminars.org/talk/Bandoleros-2021/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Ricolfi (SISSA)
DTSTART:20210212T153000Z
DTEND:20210212T173000Z
DTSTAMP:20260422T212858Z
UID:Bandoleros-2021/9
DESCRIPTION:Title: Virtual invariants of Quot schemes on 3-folds\nby Andrea Ricol
fi (SISSA) as part of V Algebraic Geometry Summer Meeting - Bandoleros 202
1\n\n\nAbstract\nLet $n > 0$ be an integer. The Quot scheme of length $n$
quotients of the free sheaf $\\mathcal{O}^r$ on affine space $\\mathbb{A}^
3$ is the main character in “rank $r$ Donaldson-Thomas theory”. We wil
l explain how to attach several types of invariants (enumerative\, cohomol
ogical\, $K-$theoretic\, motivic) to this Quot scheme\, and show that the
resulting generating functions (varying n) have nice plethystic expression
s. In particular\, the $K-$theoretic formula completely solves the higher
rank DT theory of $\\mathbb{A}^3$\, confirming the Awata-Kanno Conjecture
in String Theory. This part is joint work with Nadir Fasola and Sergej Mon
avari.\n
LOCATION:https://researchseminars.org/talk/Bandoleros-2021/9/
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