Holomorphic connections on filtered bundles over curves

  • Viktoria Heu

    IRMA UMR 7501, 7 rue René-Descartes, 67084 Strasbourg Cedex, France
  • Indranil Biswas

    School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Holomorphic connections on filtered bundles over curves cover
Download PDF

This article is published open access.

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

Viktoria Heu, Indranil Biswas, Holomorphic connections on filtered bundles over curves. Doc. Math. 18 (2013), pp. 1473–1480

DOI 10.4171/DM/433