Quasimaps to moduli spaces of sheaves on a surface

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 $\epsilon $ -stable quasimaps. We then establish reduced wall-crossing formulas which relate the reduced Gromov–Witten theory of mod...

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Bibliographic Details
Published in:Forum of mathematics. Sigma 2024-01, Vol.12, Article e61
Main Author: Nesterov, Denis
Format: Article
Language:English
Subjects:
Geometry
Sheaves
Topological manifolds
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Summary: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 $\epsilon $ -stable 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 $g(C)\leq 1$ ; Donaldson–Thomas/Pandharipande–Thomas correspondence with relative insertions on $S\times \mathbb {P}^1$ .
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2024.48