Arkadij Bojko: Equivariant Segre and Verlinde series for Quot-schemes

Abstract

Motivated by strange duality, Johnson predicted a correspondence between certain invariants called Segre and Verlinde defined using Hilbert schemes of points on a surface. In my previous work, I addressed these invariants for Quot schemes parametrizing zero-dimensional quotients of vector bundles. In doing so, I have extended the correspondence also to Calabi—Yau fourfolds and observed a new symmetry relating the invariants in dimensions 1, 2 and 4. All of these results have been formulated for compact surfaces only, which led to our joint work with Jiahui Huang where we addressed the purely equivariant setting for affine spaces. This introduces higher-degree contributions which have no compact analogues. In the talk, I will explain how Segre—Verlinde correspondence can be extended to higher-degrees by studying the structure of a more general generating series. As a consequence of our result, we obtain a prediction for the reduced correspondence back in the compact case.