Virasoro constraints for moduli spaces of sheaves on surfaces

TL;DR

This paper proposes a conjecture extending Virasoro constraints to moduli spaces of stable sheaves on surfaces, generalizing previous results on Hilbert schemes, and verifies it in multiple cases using combinatorial methods.

Contribution

It introduces a new conjecture on Virasoro constraints for sheaf moduli spaces and verifies it in various nontrivial instances.

Findings

Conjecture extends Virasoro constraints to broader moduli spaces.

Verification achieved through combinatorial description of equivariant sheaves.

Results support the conjecture's validity in multiple cases.

Abstract

We introduce a conjecture on Virasoro constraints for the moduli space of stable sheaves on a smooth projective surface. These generalise the Virasoro constraints on the Hilbert scheme of a surface found by Moreira (arXiv:2008.13746) and Moreira, Oblomkov, Okounkov and Pandharipande (arXiv:2008.12514). We verify the conjecture in many nontrivial cases by using a combinatorial description of equivariant sheaves found by Klyachko.