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arXiv · 2111.11417

Quasimaps to moduli spaces of sheaves

Denis Nesterov
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Abstract

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.

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Denis Nesterov. 2021-11-22. Quasimaps to moduli spaces of sheaves. https://doi.org/10.1017/fmp.2025.3

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