On the virtual Euler characteristics of the moduli spaces of semistable sheaves on a complex projective surface

Abstract: (warning: notice unusual time)

I'll deliver an overview of studies on the virtual Euler characteristics of the moduli spaces of semistable sheaves on a complex projective surface. The virtual Euler characteristic is a refinement of the topological Euler characteristic for a proper scheme with a perfect obstruction theory，which was introduced by Fantechi and Goettsche, and by Ciocan-Fontanine and Kapranov. Motivated by the work of Vafa and Witten in the early 90's on the S-duality conjecture in N=4 super Yang-Mills theory in physics, Goettsche and Kool conjectured that the generating function of the virtual Euler characteristics, or other variants, of the moduli space of semistable sheaves on a complex projective surfaces could be written in terms of modular forms (and the Seiberg-Witten invariants), and they verified it in examples. I'll describe the recent progress around this topic, starting by mentioning more background materials such as the studies on the topological Euler characteristics of the moduli spaces.

algebraic geometry

Audience: researchers in the topic

( slides )

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Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

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