| Speaker: | Nikolas Kuhn (University of Oslo) |
|---|---|
| Title: | Spin structures on quadratic complexes |
| Date (JST): | Tue, Apr 23, 2024, 13:30 - 15:00 |
| Place: | Seminar Room A |
| Abstract: | We present a notion of spin structure for a perfect complex E (on a complex variety X) which is equipped with an oriented quadratic structure. The existence of a spin structure on E is obstructed by a natural Z/2Z-gerbe over X, carrying a universal spin structure. As an application we show how to construct a twisted virtual structure sheaf on moduli spaces of sheaves on Calabi-Yau fourfolds, which lives on the spin gerbe over a moduli space M. We expect that - after inverting 2 in the cofficients - this defines a natural class in the K-theory of M, recovering the one defined by Oh-Thomas. |
