Geodesic
Holomorphic connections on filtered bundles over curves
Documenta mathematica, Tome 18 (2013), pp. 1473-1480.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $X$ be a compact connected Riemann surface and $E_P$ a holomorphic principal $P$--bundle over $X$, where $P$ is a parabolic subgroup of a complex reductive affine algebraic group $G$. If the Levi bundle associated to $E_P$ admits a holomorphic connection, and the reduction $E_P \subset E_P\times^P G$ is rigid, we prove that $E_P$ admits a holomorphic connection. As an immediate consequence, we obtain a sufficient condition for a filtered holomorphic vector bundle over $X$ to admit a filtration preserving holomorphic connection. Moreover, we state a weaker sufficient condition in the special case of a filtration of length two.
Classification : 14H60, 14F05, 53C07
Keywords: holomorphic connection, filtration, Atiyah bundle, parabolic subgroup 
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     author = {Biswas, Indranil and Heu, Viktoria},
     title = {Holomorphic connections on filtered bundles over curves},
     journal = {Documenta mathematica},
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     volume = {18},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a5/}
}
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Biswas, Indranil; Heu, Viktoria. Holomorphic connections on filtered bundles over curves. Documenta mathematica, Tome 18 (2013), pp. 1473-1480. http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a5/