Pure and Applied Mathematics Quarterly
Volume 17 (2021)
On multiple cover formula for local K3 gerbes
Pages: 2005 – 2080
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.
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