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A blowup formula for sheaf-theoretic virtual enumerative invariants on projective surfaces and its applications
Yuuji Tanaka , Kyoto University)
After mentioning some backgrounds, I'll talk about a blowup formula for sheaf-theoretic virtual enumerative invariants on projective surfaces and its applications at the level of the generating series of those invariants. For instance, we obtain Goettsche-Kool's conjectural blowup formulae for the generating series of the virtual Euler characteristics and virtual $\chi_y$-genera of the moduli spaces, in which modular forms appear in the same way as in Vafa-Witten's original paper in '94. This determines some of universal functions in the generating series of Vafa-Witten invariants on a projective surface, which were conjectured also by Goettsche-Kool and Goettsche-Kool-Laarakker. These are based on joint work arXiv:2107.08155 with Nikolas Kuhn and arXiv:2205.12953 with Nikolas Kuhn and Oliver Leigh.
2023-12-24 14:30-15:30
Room A-110, TSIMF
A blowup formula for sheaf-theoretic virtual enumerative invariants on projective surfaces and its applications - Yuuji Tanaka
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