Verlinde formulae on complex surfaces: K-theoretic invariants

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).

Keywords

• 14D20
• 14D21
• 14J60
• 14J80
• 14J81
• Moduli of (Higgs) sheaves on surfaces
• Verlinde formula
• K-theoretic invariants