Holomorphic Connections on Filtered Bundles over Curves
نویسندگان
چکیده
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 × P G 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. 2010 Mathematics Subject Classification: 14H60, 14F05, 53C07
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