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Refined sheaf counting on local K3 surfaces

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arxiv 2403.12741 v1 pith:CA22B2HA submitted 2024-03-19 math.AG hep-th

Richard P. Thomas This is my paper · ORCID
classification math.AGhep-th
keywords surfacescountinginvariantslocalrefinedsheafvafa-wittenalong
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The refined local Donaldson-Thomas theory of curves

    math.AG 2025-06 unverdicted novelty 8.0 of 10

    The refined K-theoretic DT and PT theories of local curves are solved explicitly via localization to skew nested Hilbert schemes, yielding three universal series from the equivariant vertex and confirming the DT/PT co...

  2. BPS polynomials and Welschinger invariants

    math.AG 2025-06 conditional novelty 7.0 of 10

    The new BPS polynomials of surfaces specialize at q=-1 to Welschinger invariants for blowups of the projective plane at up to six points.

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