# Square root Euler classes and counting sheaves on Calabi-Yau 4-folds

### Richard Thomas (Imperial College London)

25-Sep-2020, 19:00-20:00 (20 months ago)

Abstract: I will explain a nice characteristic class of $SO(2n,\mathbf{C})$ bundles in both Chow cohomology and K-theory, and how to localise it to the zeros of an isotropic section. This builds on work of Edidin-Graham, Polishchuk-Vaintrob, Anderson and many others.

This can be used to construct an algebraic virtual cycle (and virtual structure sheaf) on moduli spaces of stable sheaves on Calabi-Yau 4-folds. It recovers the real derived differential geometry virtual cycle of Borisov-Joyce but has nicer properties, like a torus localisation formula. Joint work with Jeongseok Oh (KIAS).

algebraic geometry

Audience: researchers in the topic

( slides | video )

Comments: The discussion for Richard Thomas’s talk is taking place not in zoom-chat, but at tinyurl.com/2020-09-25-rt (and will be deleted after 3-7 days).