Virasoro constraints for moduli of sheaves and vertex algebras
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Date
2024-04
Publication Type
Journal Article
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yes
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Abstract
In enumerative geometry, Virasoro constraints were first conjectured in GromovWitten theory with many new recent developments in the sheaf theoretic context. In this paper, we rephrase the sheaf theoretic Virasoro constraints in terms of primary states coming from a natural conformal vector in Joyce’s vertex algebra. This shows that Virasoro constraints are preserved under wall-crossing. As an application, we prove the conjectural Virasoro constraints for moduli spaces of torsion-free sheaves on any curve and on surfaces with only (p,p) cohomology classes by reducing the statements to the rank 1 case.
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published
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Volume
236 (1)
Pages / Article No.
387 - 476
Publisher
Springer
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Subject
14F08; 14H60; 14J60; 17B68; 17B69
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182181 - Cohomological field theories, algebraic cycles, and moduli spaces (SNF)
786580 - Moduli, algebraic cycles, and integration (EC)
786580 - Moduli, algebraic cycles, and integration (EC)