Virasoro constraints in sheaf theory and vertex algebras
October 3, 2022
In enumerative geometry, Virasoro constraints first appeared in the context of moduli of stable curves and maps. These constraints provide a rich set of conjectural relations among Gromov-Witten descendent invariants. Recently, the analogous constraints were formulated in several sheaf theoretic contexts; stable pairs on 3-folds, Hilbert scheme of points on surfaces, higher rank sheaves on surfaces with only (p,p)-cohomology. In joint work with A. Bojko, M. Moreira, we extend and reinterpret Virasoro constraints in sheaf theory using Joyce's vertex algebra. This new interpretation yields a proof of Virasoro constraints for curves and surfaces with only (p,p) cohomology by means of wall-crossing formulas.
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