Let be a compact connected Riemann surface and a holomorphic principal --bundle over , where is a parabolic subgroup of a complex reductive affine algebraic group . If the Levi bundle associated to admits a holomorphic connection, and the reduction is rigid, we prove that admits a holomorphic connection. As an immediate consequence, we obtain a sufficient condition for a filtered holomorphic vector bundle over to admit a filtration preserving holomorphic connection. Moreover, we state a weaker sufficient condition in the special case of a filtration of length two.
Cite this article
Indranil Biswas, Viktoria Heu, Holomorphic connections on filtered bundles over curves. Doc. Math. 18 (2013), pp. 1473–1480DOI 10.4171/DM/433