[Connexions d'Einstein–Hermite sur les fibrés de Higgs tordus]
Soit X une variété projective lisse sur . Nous démontrons qu'un fibré de Higgs tordu sur X possède une connexion d'Einstein–Hermite si et seulement si 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.
Let X be a smooth projective variety over . We prove that a twisted Higgs vector bundle on X admits an Einstein–Hermitian connection if and only if is polystable. A similar result for twisted vector bundles (no Higgs fields) was proved in Wang [10]. Our approach is simpler.
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@article{CRMATH_2010__348_17-18_981_0,
author = {Biswas, Indranil and G\'omez, Tom\'as L. and Hoffmann, Norbert and Hogadi, Amit},
title = {Einstein{\textendash}Hermitian connection on twisted {Higgs} bundles},
journal = {Comptes Rendus. Math\'ematique},
pages = {981--983},
publisher = {Elsevier},
volume = {348},
number = {17-18},
year = {2010},
doi = {10.1016/j.crma.2010.07.027},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.07.027/}
}
TY - JOUR AU - Biswas, Indranil AU - Gómez, Tomás L. AU - Hoffmann, Norbert AU - Hogadi, Amit TI - Einstein–Hermitian connection on twisted Higgs bundles JO - Comptes Rendus. Mathématique PY - 2010 SP - 981 EP - 983 VL - 348 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.07.027/ DO - 10.1016/j.crma.2010.07.027 LA - en ID - CRMATH_2010__348_17-18_981_0 ER -
%0 Journal Article %A Biswas, Indranil %A Gómez, Tomás L. %A Hoffmann, Norbert %A Hogadi, Amit %T Einstein–Hermitian connection on twisted Higgs bundles %J Comptes Rendus. Mathématique %D 2010 %P 981-983 %V 348 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.07.027/ %R 10.1016/j.crma.2010.07.027 %G en %F CRMATH_2010__348_17-18_981_0
Biswas, Indranil; Gómez, Tomás L.; Hoffmann, Norbert; Hogadi, Amit. Einstein–Hermitian connection on twisted Higgs bundles. Comptes Rendus. Mathématique, Tome 348 (2010) no. 17-18, pp. 981-983. doi : 10.1016/j.crma.2010.07.027. http://www.numdam.org/articles/10.1016/j.crma.2010.07.027/
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