Geodesic
Holomorphic connections on filtered bundles over curves
Documenta mathematica, Tome 18 (2013), pp. 1473-1480
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Let X be a compact connected Riemann surface and EP​ 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 EP​ admits a holomorphic connection, and the reduction EP​⊂EP​×PG is rigid, we prove that EP​ 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.
DOI : 10.4171/dm/433
Classification : 14H60, 53C07
Mots-clés : holomorphic connection, filtration, Atiyah bundle, parabolic subgroup 
@article{10_4171_dm_433,
     author = {Viktoria Heu and Indranil Biswas},
     title = {Holomorphic connections on filtered bundles over curves},
     journal = {Documenta mathematica},
     pages = {1473--1480},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/433},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/433/}
}
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Viktoria Heu; Indranil Biswas. Holomorphic connections on filtered bundles over curves. Documenta mathematica, Tome 18 (2013), pp. 1473-1480. doi: 10.4171/dm/433

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