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arXiv · 2404.12723

Virasoro constraints for K3 surfaces and monodromy operators

Weisheng Wang
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Abstract

The Virasoro constraints for moduli spaces of stable torsion free sheaves on a surface with only $(p,p)$-cohomology were recently proved by Bojko-Moreira-Lim. The rank 1 case, which is not restricted to surfaces with only $(p,p)$-cohomology, was established by Moreira. We prove Virasoro constraints for K3 surfaces using Markman monodromy operators, which allow us to reduce to the rank 1 case. We also prove new Virasoro constraints in rank 0. Finally, for K3 surfaces, we introduce new Virasoro operators in negative degree which, together with the previous Virasoro operators, give a representation of Virasoro algebra with central charge $24$.

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Weisheng Wang. 2024-04-19. Virasoro constraints for K3 surfaces and monodromy operators. https://arxiv.org/abs/2404.12723

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