Comptes Rendus
no. 21-22
Analytic Geometry
Semistability of invariant bundles over G/Γ
[Semi-stabilité de fibrés invariants sur G/Γ]

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. 21-22, pp. 1187-1190.

Soit Γ un sous-groupe discret cocompact dʼun groupe algébique réductif affine G. Nous démontrons que tout fibré invariant sur G/Γ est semi-stable.

Let G be a connected reductive affine algebraic group defined over C, and let Γ be a cocompact lattice in G. We prove that any invariant bundle on G/Γ is semistable.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.10.022
Indranil Biswas 1

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India 
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Indranil Biswas. Semistability of invariant bundles over $ G/\Gamma $. Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1187-1190. doi : 10.1016/j.crma.2011.10.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.10.022/

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[2] I. Biswas Stable Higgs bundles on compact Gauduchon manifolds, C. R. Acad. Sci. Paris, Ser. I, Volume 349 (2011), pp. 71-74

[3] I. Biswas Principal bundles on compact complex manifolds with trivial tangent bundle, Arch. Math. (Basel), Volume 96 (2011), pp. 409-416

[4] L. Bruasse Harder–Narasimhan filtration on non Kähler manifolds, Int. J. Math., Volume 12 (2001), pp. 579-594

[5] S. Kobayashi Differential Geometry of Complex Vector Bundles, Publ. Math. Soc. Japan, vol. 15, Iwanami Shoten Publishers and Princeton University Press, 1987

[6] A. Ramanathan Stable principal bundles on a compact Riemann surface, Math. Ann., Volume 213 (1975), pp. 129-152

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