Holomorphic connections on filtered bundles over curves

  • Indranil Biswas

    School of Mathematics IRMA Tata Institute of Fundamental UMR 7501 Research 7 rue René-Descartes Homi Bhabha Road 67084 Strasbourg Cedex Bombay 400005 France India
  • Viktoria Heu

    School of Mathematics IRMA Tata Institute of Fundamental UMR 7501 Research 7 rue René-Descartes Homi Bhabha Road 67084 Strasbourg Cedex Bombay 400005 France India
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Abstract

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. 1473–1480

DOI 10.4171/DM/433