On multiple cover formula for local K3 gerbes
Yunfeng Jiang, Hsian-Hua Tseng
TL;DR
This paper extends the multiple cover formula for counting invariants from local K3 surfaces to twisted cases, enabling proofs of S-duality conjectures for K3 surfaces.
Contribution
It generalizes Toda's multiple cover formula to twisted sheaves on local K3 surfaces, providing a new tool for studying invariants and dualities.
Findings
Generalized multiple cover formula to twisted sheaves
Proved S-duality conjecture for K3 surfaces using the formula
Enhanced understanding of invariants in algebraic geometry
Abstract
We generalize the multiple cover formula of Y. Toda (proved by Maulik-Thomas) for counting invariants for semistable coherent sheaves on local K3 surfaces to semistable twisted sheaves over twisted local K3 surfaces. The formula has an application to prove any rank S-duality conjecture for K3 surfaces.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry