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Verlinde formulae on complex surfaces: K-theoretic invariants

Published online by Cambridge University Press:  11 January 2021

L. Göttsche
Affiliation:
Mathematics Group, International Centre for Theoretical Physics, Strada Costiera 11, 34100, Trieste, Italy; E-mail: gottsche@ictp.it.
M. Kool
Affiliation:
Mathematical Institute, Utrecht University, P.O. Box 80010, 3508 TA, Utrecht, The Netherlands; E-mail: m.kool1@uu.nl.
R. A. Williams
Affiliation:
University of the Bahamas, Department of Mathematics, University Drive, Nassau, The Bahamas; E-mail: runako.williams@ub.edu.bs.

Abstract

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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).

Type
Algebraic and Complex Geometry
Creative Commons
Creative Common License - CCCreative Common License - BY
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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