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arXiv · 1903.03869

Verlinde formulae on complex surfaces: K-theoretic invariants

L. Göttsche·M. Kool·R. A. Williams
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Abstract

We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between $K$-theoretic Donaldson invariants studied by the first named author and Nakajima-Yoshioka and $K$-theoretic Vafa-Witten invariants introduced by Thomas and also studied by the first and second named authors. We verify our conjectures in many examples (e.g. on K3 surfaces).

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BibTeXRIS

L. Göttsche, M. Kool, R. A. Williams. 2019-03-09. Verlinde formulae on complex surfaces: K-theoretic invariants. https://doi.org/10.1017/fms.2020.50

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