2024/04/19 by Weisheng Wang, Wang, Weisheng
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Holomorphic and Operator Theory #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2404.12723
openalex publication_date 2024/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.