Analytic Geometry
Semistability of invariant bundles over G/Γ
[Semi-stabilité de fibrés invariants sur G/Γ]
Comptes Rendus. Mathématique, Tome 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
Biswas, Indranil 1

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
@article{CRMATH_2011__349_21-22_1187_0,
     author = {Biswas, Indranil},
     title = {Semistability of invariant bundles over $ G/\Gamma $},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1187--1190},
     publisher = {Elsevier},
     volume = {349},
     number = {21-22},
     year = {2011},
     doi = {10.1016/j.crma.2011.10.022},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2011.10.022/}
}
TY  - JOUR
AU  - Biswas, Indranil
TI  - Semistability of invariant bundles over $ G/\Gamma $
JO  - Comptes Rendus. Mathématique
PY  - 2011
SP  - 1187
EP  - 1190
VL  - 349
IS  - 21-22
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2011.10.022/
DO  - 10.1016/j.crma.2011.10.022
LA  - en
ID  - CRMATH_2011__349_21-22_1187_0
ER  - 
%0 Journal Article
%A Biswas, Indranil
%T Semistability of invariant bundles over $ G/\Gamma $
%J Comptes Rendus. Mathématique
%D 2011
%P 1187-1190
%V 349
%N 21-22
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2011.10.022/
%R 10.1016/j.crma.2011.10.022
%G en
%F CRMATH_2011__349_21-22_1187_0
Biswas, Indranil. Semistability of invariant bundles over $ G/\Gamma $. Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1187-1190. doi : 10.1016/j.crma.2011.10.022. http://www.numdam.org/articles/10.1016/j.crma.2011.10.022/

[1] Atiyah, M.F. Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc., Volume 85 (1957), pp. 181-207

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

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

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

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

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

Cité par Sources :