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- W4286851149 abstract "This article is the first in a series of three articles, the aim of which is to study various correspondences between four enumerative theories associated to a surface $S$: Gromov-Witten theory of $S^{[n]}$, orbifold Gromov-Witten theory of $[S^{(n)}]$, relative Gromov-Witten theory of $Stimes C$ for a nodal curve $C$ and relative Donaldson-Thomas theory of $Stimes C$. In this article, we develop a theory of quasimaps to moduli spaces of sheaves on a surface. Under some natural assumptions, we prove that moduli spaces of quasimaps are proper and carry a perfect obstruction theory. Moreover, moduli spaces of quasimaps are naturally isomorphic to relative moduli spaces of sheaves. Using Zhou's theory of calibrated tails, we establish a wall-crossing formula which relate Gromov-Witten theory of $S^{[n]}$ and relative Donaldson-Thomas theory of $Stimes C$. As an application, we prove that quantum cohomology of $S^{[n]}$ is determined by relative Pandharipande-Thomas theory of $Stimes mathbb{P}^1$, if $S$ is a del Pezzo surface, conjectured by Maulik." @default.
- W4286851149 created "2022-07-25" @default.
- W4286851149 creator A5041558892 @default.
- W4286851149 date "2021-11-22" @default.
- W4286851149 modified "2023-10-17" @default.
- W4286851149 title "Quasimaps to moduli spaces of sheaves" @default.
- W4286851149 doi "https://doi.org/10.48550/arxiv.2111.11417" @default.
- W4286851149 hasPublicationYear "2021" @default.
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