Verlinde formulae on complex surfaces: K-theoretic invariants. (11th January 2021)

• Record Type: Journal Article
• Authors: Göttsche, L.; Kool, M.; Williams, R. A.
• Is Part Of: Forum of mathematics. Volume 9(2021)
• Publication Date: 2021-01-11
• Subjects: 14D20, -- 14D21, -- 14J60, -- 14J80, -- 14J81; Moduli of (Higgs) sheaves on surfaces, -- Verlinde formula, -- K-theoretic invariants; Mathematics -- Periodicals; 510
• DOI: 10.1017/fms.2020.50
• Languages: English
• ISSNs: 2050-5094

Abstract

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).