Motives of moduli spaces of bundles on curves
Organizers
Speaker
Victoria Hoskins
Time
Thursday, January 9, 2025 3:00 PM - 4:00 PM
Venue
A7-201
Online
Zoom 638 227 8222
(BIMSA)
Abstract
Enumerative geometry often exploits the fact that certain moduli spaces of bundles (and sheaves) have tautologically generated cohomology. In this talk I will discuss a motivic incarnation of the above tautological generation for moduli spaces of bundles on curves. Motives are a way to encode various cohomological information and can also be used to describe algebraic cycles. I will explain that the motives of moduli spaces of (semistable) Higgs and vector bundles on a curve with coprime rank and degree are generated by the motive of the curve. For SL-Higgs moduli spaces, which are non-tautologically generated, we additionally need motives of certain étale covers of the curve. We will also see how to exploit the fact that these moduli spaces have abelian motives to produce motivic formulas in low rank and provide motivic lifts of known cohomological phenomena, such as chi-independence and mirror symmetry.
This is joint work with Simon Pepin Lehalleur and partially also with Lie Fu.
This is joint work with Simon Pepin Lehalleur and partially also with Lie Fu.