Comptes Rendus
Algebraic Geometry
Einstein–Hermitian connection on twisted Higgs bundles
Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 981-983.

Let X be a smooth projective variety over C. We prove that a twisted Higgs vector bundle (E,θ) on X admits an Einstein–Hermitian connection if and only if (E,θ) is polystable. A similar result for twisted vector bundles (no Higgs fields) was proved in Wang [10]. Our approach is simpler.

Soit X une variété projective lisse sur C. Nous démontrons qu'un fibré de Higgs tordu (E,θ) sur X possède une connexion d'Einstein–Hermite si et seulement si (E,θ) est polystable. Un résultat analogue pour les fibrés vectoriels (dépourvus d'un champ de Higgs) a été démontré dans Wang [10]. Notre approche est plus simple.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2010.07.027

Indranil Biswas 1; Tomás L. Gómez 2, 3; Norbert Hoffmann 4; Amit Hogadi 1

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
2 Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Serrano 113bis, 28006 Madrid, Spain
3 Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
4 Mathematisches Institut der Freien Universität, Arnimallee 3, 14195 Berlin, Germany
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Indranil Biswas; Tomás L. Gómez; Norbert Hoffmann; Amit Hogadi. Einstein–Hermitian connection on twisted Higgs bundles. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 981-983. doi : 10.1016/j.crma.2010.07.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.027/

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