On the virtual Euler characteristics of the moduli spaces of semistable sheaves on a complex projective surface
Location
(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.
The discussion for Yuuji Tanaka’s talk is taking place not in zoom-chat, but at https://tinyurl.com/2021-03-12-yt (and will be deleted after ~3-7 days).