[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.
Accepté le :
Publié le :
Indranil Biswas 1 ; Tomás L. Gómez 2, 3 ; Norbert Hoffmann 4 ; Amit Hogadi 1
@article{CRMATH_2010__348_17-18_981_0, author = {Indranil Biswas and Tom\'as L. G\'omez and Norbert Hoffmann and Amit Hogadi}, 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}, }
TY - JOUR AU - Indranil Biswas AU - Tomás L. Gómez AU - Norbert Hoffmann AU - Amit Hogadi 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 DO - 10.1016/j.crma.2010.07.027 LA - en ID - CRMATH_2010__348_17-18_981_0 ER -
Indranil Biswas; Tomás L. Gómez; Norbert Hoffmann; Amit Hogadi. Einstein–Hermitian connection on twisted Higgs bundles. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 981-983. doi : 10.1016/j.crma.2010.07.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.027/
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