Stable bundles on hypercomplex surfaces

Details Stable bundles on hypercomplex surfaces Stable bundles on hypercomplex surfaces

2006-11-23

arxiv.org/abs/math/0611714v3

Cent. Eur. J. Math. 8 (2010), no. 2, 327--337

Mathematics

Differential Geometry

17 pages. Version 3.0: reference added

Scientific paper

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 hyperkaehler 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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