Virasoro constraints on moduli of sheaves and vertex algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| 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 |