Comptes Rendus
no. 1-2
Analytic Geometry
Stable Higgs bundles on compact Gauduchon manifolds
[Les fibrés de Higgs stables sur les variétés de Gauduchon]

Présenté par : Jean-Pierre Demailly

Indranil Biswas1
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 71-74.

Soit M une variété complexe compacte muni d'une métrique de Gauduchon. Si TM est holomorphiquement trivial, et (V,θ) est un fibré SL(r,C)-Higgs stable, alors on démontre que θ=0. On démontre que la correspondance entre les fibrés de Higgs et les représentations du groupe fondamental pour une variété kählerienne compacte ne s'étend pas aux variétés de Gauduchon. Ceci est accompli en appliquant le résultat ci-dessus à Γ\G, où Γ est un sous-groupe discret, sans torsion et co-compact d'un groupe semi-simple complexe G.

Let M be a compact complex manifold equipped with a Gauduchon metric. If TM is holomorphically trivial, and (V,θ) is a stable SL(r,C)-Higgs bundle on M, then we show that θ=0. We show that the correspondence between Higgs bundles and representations of the fundamental group for a compact Kähler manifold does not extend to compact Gauduchon manifolds. This is done by applying the above result to Γ\G, where Γ is a discrete torsionfree cocompact subgroup of a complex semisimple group G.

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Accepté le :
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DOI : 10.1016/j.crma.2010.11.010
Indranil Biswas 1

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India 
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Indranil Biswas. Stable Higgs bundles on compact Gauduchon manifolds. Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 71-74. doi : 10.1016/j.crma.2010.11.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.010/

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