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- W4301089237 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 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." @default.
- W4301089237 created "2022-10-04" @default.
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- W4301089237 date "2006-11-22" @default.
- W4301089237 modified "2023-10-16" @default.
- W4301089237 title "Stable bundles on hypercomplex surfaces" @default.
- W4301089237 doi "https://doi.org/10.48550/arxiv.math/0611714" @default.
- W4301089237 hasPublicationYear "2006" @default.
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