Descendent series for Hilbert schemes of points on surfaces

Abstract: Structure often emerges from Hilbert schemes of points on varieties when the underlying variety is fixed but the number of points parametrized varies. Some examples of such structure come from integrals of tautological bundles, which arise in geometric and physical computations. When compiled into generating series, these integrals display interesting functional properties. I will give an overview of results on such series; the focus will be on K-theoretic descendent series for Hilbert schemes on surfaces, certain series formed from holomorphic Euler characteristics of tautological bundles. In particular, I will explain how to see that the K-theoretic descendent series are expansions of rational functions.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html