Stable bundles on hypercomplex surfaces

• Autorzy: Ruxandra Moraru , Misha Verbitsky
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Hopf surface; Stable bundles; Instanton bundles; Hypercomplex; Generalized hyperkaehler

Kategorie tematyczne

• 53C80: Applications to physics
• 53C26: Hyper-K\"ahler and quaternionic K\"ahler geometry, ``special'' geometry
• 32L05: Holomorphic bundles and generalizations
• 53C55: Hermitian and K\"ahlerian manifolds
• 14D21: Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 2
• Strony: 327-337

Daty

wydano

2010-04-01

online

2010-04-14

Twórcy

autor

Ruxandra Moraru

• University of Waterloo

autor

Misha Verbitsky

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Identyfikatory

DOI

10.2478/s11533-010-0006-7