[Les fibrés de Higgs stables sur les variétés de Gauduchon]
Soit M une variété complexe compacte muni d'une métrique de Gauduchon. Si TM est holomorphiquement trivial, et est un fibré -Higgs stable, alors on démontre que . 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 , 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 is a stable -Higgs bundle on M, then we show that . 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 , where Γ is a discrete torsionfree cocompact subgroup of a complex semisimple group G.
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@article{CRMATH_2011__349_1-2_71_0,
author = {Biswas, Indranil},
title = {Stable {Higgs} bundles on compact {Gauduchon} manifolds},
journal = {Comptes Rendus. Math\'ematique},
pages = {71--74},
publisher = {Elsevier},
volume = {349},
number = {1-2},
year = {2011},
doi = {10.1016/j.crma.2010.11.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.11.010/}
}
TY - JOUR AU - Biswas, Indranil TI - Stable Higgs bundles on compact Gauduchon manifolds JO - Comptes Rendus. Mathématique PY - 2011 SP - 71 EP - 74 VL - 349 IS - 1-2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.11.010/ DO - 10.1016/j.crma.2010.11.010 LA - en ID - CRMATH_2011__349_1-2_71_0 ER -
Biswas, Indranil. Stable Higgs bundles on compact Gauduchon manifolds. Comptes Rendus. Mathématique, Tome 349 (2011) no. 1-2, pp. 71-74. doi : 10.1016/j.crma.2010.11.010. http://www.numdam.org/articles/10.1016/j.crma.2010.11.010/
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