Stable bundles on hypercomplex surfaces

Moraru, R. and Verbitski, M. (2010) Stable bundles on hypercomplex surfaces. Central European Journal of Mathematics, 8(2), pp. 327-337. (doi: 10.2478/s11533-010-0006-7)

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Verbitski, Dr Mikhail
Authors: Moraru, R., and Verbitski, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Central European Journal of Mathematics
ISSN (Online):1644-3616

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
316541Hyperkaehler manifoldsMikhail VerbitskiEngineering & Physical Sciences Research Council (EPSRC)GR/R77773/01Mathematics