Refined sheaf counting on local K3 surfaces
arXiv:2403.12741
Abstract
We compute all refined sheaf counting invariants -- Vafa-Witten, reduced DT, stable pairs and Gopakumar-Vafa -- for all classes on local surfaces. Along the way we develop rank 0 Vafa-Witten theory on surfaces. An important feature of the calculation is that the ``instanton contribution" -- of sheaves supported scheme theoretically on -- to any of the invariants depends only on the square of the class, not its divisibility.
16 pages