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arXiv · 2403.12741

Refined sheaf counting on local K3 surfaces

Richard P. Thomas
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Abstract

We compute all refined sheaf counting invariants -- Vafa-Witten, reduced DT, stable pairs and Gopakumar-Vafa -- for all classes on local $K3$ surfaces. Along the way we develop rank 0 Vafa-Witten theory on $K3$ surfaces. An important feature of the calculation is that the ``instanton contribution" -- of sheaves supported scheme theoretically on $S$ -- to any of the invariants depends only on the square of the class, not its divisibility.

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Richard P. Thomas. 2024-03-19. Refined sheaf counting on local K3 surfaces. https://arxiv.org/abs/2403.12741

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