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arXiv · 1806.02657

Sheaf counting on local K3 surfaces

Davesh Maulik·Richard P. Thomas
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Abstract

There are two natural ways to count stable pairs or Joyce-Song pairs on $X=\mathrm{K3}\times\mathbb C$; one via weighted Euler characteristic and the other by virtual localisation of the reduced virtual class. Since $X$ is noncompact these need not be the same. We show their generating series are related by an exponential. As applications we prove two conjectures of Toda, and a conjecture of Tanaka-Thomas defining Vafa-Witten invariants in the semistable case.

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Davesh Maulik, Richard P. Thomas. 2019-12-03. Sheaf counting on local K3 surfaces. https://doi.org/10.4310/pamq.2018.v14.n3.a1

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