Verlinde formulae on complex surfaces: K-theoretic invariants
Algebraic Geometry
2025-04-09 v2 High Energy Physics - Theory
Differential Geometry
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 -theoretic Donaldson invariants studied by the first named author and Nakajima-Yoshioka and -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).
Cite
@article{arxiv.1903.03869,
title = {Verlinde formulae on complex surfaces: K-theoretic invariants},
author = {L. Göttsche and M. Kool and R. A. Williams},
journal= {arXiv preprint arXiv:1903.03869},
year = {2025}
}
Comments
Published version. 37 pages