Quasimaps to moduli spaces of sheaves on a $K3$ surface
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866915203790143488 |
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| author | Nesterov, Denis |
| author_facet | Nesterov, Denis |
| contents | In this article, we study quasimaps to moduli spaces of sheaves on a $K3$ surface $S$. We construct a surjective cosection of the obstruction theory of moduli spaces of quasimaps. We then establish reduced wall-crossing formulas which relate the reduced Gromov-Witten theory of moduli spaces of sheaves on $S$ and the reduced Donaldson-Thomas theory of $S\times C$, where $C$ is a nodal curve. As applications, we prove the Hilbert-schemes part of the Igusa cusp form conjecture; higher-rank/rank-one Donaldson-Thomas correspondence with relative insertions on $S\times C$, if $g(C)\leq1$; Donaldson-Thomas/Pandharipande-Thomas correspondence with relative insertions on $S\times \mathbb{P}^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_11425 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quasimaps to moduli spaces of sheaves on a $K3$ surface Nesterov, Denis Algebraic Geometry In this article, we study quasimaps to moduli spaces of sheaves on a $K3$ surface $S$. We construct a surjective cosection of the obstruction theory of moduli spaces of quasimaps. We then establish reduced wall-crossing formulas which relate the reduced Gromov-Witten theory of moduli spaces of sheaves on $S$ and the reduced Donaldson-Thomas theory of $S\times C$, where $C$ is a nodal curve. As applications, we prove the Hilbert-schemes part of the Igusa cusp form conjecture; higher-rank/rank-one Donaldson-Thomas correspondence with relative insertions on $S\times C$, if $g(C)\leq1$; Donaldson-Thomas/Pandharipande-Thomas correspondence with relative insertions on $S\times \mathbb{P}^1$. |
| title | Quasimaps to moduli spaces of sheaves on a $K3$ surface |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2111.11425 |