Quasimaps to moduli spaces of sheaves
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866915212160925696 |
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| author | Nesterov, Denis |
| author_facet | Nesterov, Denis |
| contents | We develop a theory of quasimaps to a moduli space of sheaves $M$ on a surface $S$. Under some assumptions, we prove that moduli spaces of quasimaps are proper and carry a perfect obstruction theory. Moreover, they are naturally isomorphic to moduli spaces of sheaves on threefolds $S\times C$, where $C$ is a nodal curve. Using Zhou's theory of entangled tails, we establish a wall-crossing formula which therefore relates the Gromov-Witten theory of $M$ and the Donaldson-Thomas theory of $S\times C$ with relative insertions. We evaluate the wall-crossing formula for Hilbert schemes of points $S^{[n]}$, if $S$ is a del Pezzo surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_11417 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quasimaps to moduli spaces of sheaves Nesterov, Denis Algebraic Geometry We develop a theory of quasimaps to a moduli space of sheaves $M$ on a surface $S$. Under some assumptions, we prove that moduli spaces of quasimaps are proper and carry a perfect obstruction theory. Moreover, they are naturally isomorphic to moduli spaces of sheaves on threefolds $S\times C$, where $C$ is a nodal curve. Using Zhou's theory of entangled tails, we establish a wall-crossing formula which therefore relates the Gromov-Witten theory of $M$ and the Donaldson-Thomas theory of $S\times C$ with relative insertions. We evaluate the wall-crossing formula for Hilbert schemes of points $S^{[n]}$, if $S$ is a del Pezzo surface. |
| title | Quasimaps to moduli spaces of sheaves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2111.11417 |