Article contents
Verlinde formulae on complex surfaces: K-theoretic invariants
Published online by Cambridge University Press: 11 January 2021
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).
MSC classification
- Type
- Algebraic and Complex Geometry
- Information
- Creative Commons
- Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Copyright
- © The Author(s), 2020. Published by Cambridge University Press
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