Verlinde formulae on complex surfaces: K-theoretic invariants. (11th January 2021) - Göttsche, L.; Kool, M.; Williams, R. A.
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 Göttsche and Nakajima-Yoshioka and K -theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).