Virasoro constraints for moduli of sheaves and vertex algebras

• 成果类型: Article
• 署名作者: Bojko, Arkadij; Lim, Woonam; Moreira, Miguel
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01245-5
• 发表日期: 2024
• 页码: 387-476
• 关键词: donaldson-thomas theory; gromov-witten theory; topological k-theory; abelian categories; configurations; COHOMOLOGY; INVARIANTS; SPACES

摘要

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)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,p)$\end{document} cohomology classes by reducing the statements to the rank 1 case.