Quasimaps to moduli spaces of sheaves on a $K3$ surface
Forum of Mathematics, Sigma, Tome 12 (2024)
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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 $S\times \mathbb {P}^1$.
@article{10_1017_fms_2024_48,
author = {Denis Nesterov},
title = {Quasimaps to moduli spaces of sheaves on a $K3$ surface},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {12},
year = {2024},
doi = {10.1017/fms.2024.48},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.48/}
}
Denis Nesterov. Quasimaps to moduli spaces of sheaves on a $K3$ surface. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.48
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