Monopole contributions to refined Vafa-Witten invariants

Abstract

We study the monopole contribution to the refined Vafa-Witten invariant, recently defined by Maulik and Thomas [13]. We apply results of Gholampour and Thomas [7] to prove a universality result for the generating series of contributions of Higgs pairs with 1-dimensional weight spaces. For prime rank, these account for the entire monopole contribution, by a theorem of Thomas. We use toric computations to determine part of the generating series, and find agreement with the conjectures of Göttsche and Kool [10] for rank 2 and 3.

39 pages; many major and minor modifications; added proof of conjecture on universal series A

References in corpus (2)

• Equivariant K-theory and refined Vafa-Witten invariants
• Degeneracy loci, virtual cycles and nested Hilbert schemes II

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