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Stable bundles on hypercomplex surfaces

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Moraru R., Verbitsky M.

Open Mathematics

2010

tom 8

nr 2

327-337

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.

Ograniczanie wyników

1 Open Mathematics

1 Moraru R.

1 Verbitsky M.

1 2010

Wyniki wyszukiwania

Stable bundles on hypercomplex surfaces