Virasoro constraints for moduli spaces of sheaves on surfaces

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.