Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 5

On multiple cover formula for local K3 gerbes

Pages: 2005 – 2080

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n5.a10

Authors

Yunfeng Jiang (Department of Mathematics, University of Kansas, Lawrence, Ks., U.S.A.)

Hsian-Hua Tseng (Department of Mathematics, Ohio State University, Columbus, Oh., U.S.A.)

Abstract

We generalize the multiple cover formula of Y. Toda (proved by Maulik–Thomas) for counting invariants of semistable coherent sheaves on local K3 surfaces to semistable twisted sheaves on twisted local K3 surfaces. The formula has an application to prove any rank S-duality conjecture for K3 surfaces.

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Yunfeng Jiang is partially supported by NSF DMS-1600997.

Hsian-Hua Tseng is supported in part by a Simons Foundation collaboration grant.

Received 31 May 2021

Received revised 15 September 2021

Accepted 8 October 2021

Published 26 January 2022