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Stable bundles on hypercomplex surfaces

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Central European Journal of Mathematics

Abstract

A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite torsion. In the language of Hitchin’s and Gualtieri’s generalized complex geometry, (4,4)-manifolds are called “generalized hyperkähler manifolds”. We show that the moduli space of anti-self-dual connections on M is a (4,4)-manifold if M is equipped with a (4,4)-structure.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Waterloo, University Avenue West, Waterloo, ON, Canada

    Ruxandra Moraru

  2. Department of Mathematics, University of Glasgow, Glasgow, Scotland

    Misha Verbitsky

  3. Institute of Theoretical and Experimental Physics, Moscow, Russia

    Misha Verbitsky

Authors
  1. Ruxandra Moraru
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  2. Misha Verbitsky
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Correspondence to Ruxandra Moraru.

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Moraru, R., Verbitsky, M. Stable bundles on hypercomplex surfaces. centr.eur.j.math. 8, 327–337 (2010). https://doi.org/10.2478/s11533-010-0006-7

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  • DOI: https://doi.org/10.2478/s11533-010-0006-7

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