Stable bundles on hypercomplex surfaces

Ruxandra Moraru; Misha Verbitsky

Open Mathematics (2010)

  • Volume: 8, Issue: 2, page 327-337
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Ruxandra Moraru, and Misha Verbitsky. "Stable bundles on hypercomplex surfaces." Open Mathematics 8.2 (2010): 327-337. <http://eudml.org/doc/269722>.

@article{RuxandraMoraru2010,
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 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.},
author = {Ruxandra Moraru, Misha Verbitsky},
journal = {Open Mathematics},
keywords = {Hopf surface; Stable bundles; Instanton bundles; Hypercomplex; Generalized hyperkaehler; stable bundles; hypercomplex manifolds; instantons; generalized hyper-Kähler structures},
language = {eng},
number = {2},
pages = {327-337},
title = {Stable bundles on hypercomplex surfaces},
url = {http://eudml.org/doc/269722},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Ruxandra Moraru
AU - Misha Verbitsky
TI - Stable bundles on hypercomplex surfaces
JO - Open Mathematics
PY - 2010
VL - 8
IS - 2
SP - 327
EP - 337
AB - 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.
LA - eng
KW - Hopf surface; Stable bundles; Instanton bundles; Hypercomplex; Generalized hyperkaehler; stable bundles; hypercomplex manifolds; instantons; generalized hyper-Kähler structures
UR - http://eudml.org/doc/269722
ER -

References

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