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SUMMARY:Barbara Fantechi (SISSA)
DTSTART;VALUE=DATE-TIME:20201016T190000Z
DTEND;VALUE=DATE-TIME:20201016T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060756Z
UID:agstanford/30
DESCRIPTION:Title: Infinitesimal deformations of semi-smooth varieties\nby Barbara Fa
ntechi (SISSA) as part of Stanford algebraic geometry seminar\n\n\nAbstrac
t\nThis is a report on joint work with Marco Franciosi and Rita Pardini. G
eneralizing the standard definition for surfaces\, we call a variety $X$ (
over an alg closed field of char not 2) {\\em semi-smooth} if its singular
ities are \\'etale locally either $uv=0$ or $u^2=v^2w$ (pinch point)\; equ
ivalently\, if $X$ can be obtained by gluing a smooth variety (the normali
zation of $X$) along an involution (with smooth quotient) on a smooth divi
sor. They are the simplest singularities for non normal\, KSBA-stable surf
aces.\nFor a semi-smooth variety $X$\, we calculate the tangent sheaf $T_X
$ and the infinitesimal deformations sheaf ${\\mathcal T}^1_X:={\\mathcal
E}xt^1(\\Omega_X\,\\mathcal O_X)$ which determine the infinitesimal deform
ations and smoothability of $X$.\nAs an application\, we use Tziolas' form
al smoothability criterion to show that every stable semi-smooth Godeaux s
urface (classified by Franciosi\, Pardini and S\\"onke) corresponds to a s
mooth point of the KSBA moduli space\, in the closure of the open locus of
smooth surfaces.\n\nThe discussion for Barbara Fantechi’s talk is takin
g place not in zoom-chat\, but at https://tinyurl.com/2020-10-16-bf (and
will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/30/
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