Virasoro constraints on moduli of sheaves and vertex algebras

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Bojko, Arkadij, Lim, Woonam, Moreira, Miguel
Format: Preprint
Published: 2022
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916128861716480
author Bojko, Arkadij
Lim, Woonam
Moreira, Miguel
author_facet Bojko, Arkadij
Lim, Woonam
Moreira, Miguel
contents In enumerative geometry, Virasoro constraints were first conjectured in Gromov-Witten 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.
format Preprint
id arxiv_https___arxiv_org_abs_2210_05266
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Virasoro constraints on moduli of sheaves and vertex algebras
Bojko, Arkadij
Lim, Woonam
Moreira, Miguel
Algebraic Geometry
Mathematical Physics
Combinatorics
K-Theory and Homology
Representation Theory
In enumerative geometry, Virasoro constraints were first conjectured in Gromov-Witten 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.
title Virasoro constraints on moduli of sheaves and vertex algebras
topic Algebraic Geometry
Mathematical Physics
Combinatorics
K-Theory and Homology
Representation Theory
url https://arxiv.org/abs/2210.05266