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SUMMARY:Yuuji Tanaka (Kyoto University)
DTSTART;VALUE=DATE-TIME:20210313T000000Z
DTEND;VALUE=DATE-TIME:20210313T010000Z
DTSTAMP;VALUE=DATE-TIME:20240222T175808Z
UID:agstanford/42
DESCRIPTION:Title: On the virtual Euler characteristics of the moduli spaces of semistab
le sheaves on a complex projective surface\nby Yuuji Tanaka (Kyoto Uni
versity) as part of Stanford algebraic geometry seminar\n\n\nAbstract\n(wa
rning: notice unusual time)\n\nI'll deliver an overview of studies on the
virtual Euler \ncharacteristics of the moduli spaces of semistable sheave
s on a complex \nprojective surface. The virtual Euler characteristic is a
refinement of \nthe topological Euler characteristic for a proper scheme
with a perfect \nobstruction theory，which was introduced by Fantechi and
Goettsche\, and \nby Ciocan-Fontanine and Kapranov. Motivated by the work
of Vafa and \nWitten in the early 90's on the S-duality conjecture in N=4
super \nYang-Mills theory in physics\, Goettsche and Kool conjectured tha
t the \ngenerating function of the virtual Euler characteristics\, or othe
r \nvariants\, of the moduli space of semistable sheaves on a complex \npr
ojective surfaces could be written in terms of modular forms (and the \nSe
iberg-Witten invariants)\, and they verified it in examples. I'll \ndescri
be the recent progress around this topic\, starting by mentioning \nmore b
ackground materials such as the studies on the topological Euler \ncharact
eristics of the moduli spaces.\n
LOCATION:https://researchseminars.org/talk/agstanford/42/
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