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Proceedings - Mathematical Sciences

, Volume 124, Issue 4, pp 487–496 | Cite as

Meromorphic connections on vector bundles over curves

  • INDRANIL BISWAS
  • VIKTORIA HEUEmail author
Article
  • 101 Downloads

Abstract

We give a criterion for filtered vector bundles over curves to admit a filtration preserving meromorphic connection that induces a given meromorphic connection on the corresponding graded bundle.

Keywords

Meromorphic connection filtered bundle Atiyah bundle 

2000 Mathematics Subject Classification

14H60 14F05 53C07. 

Notes

Acknowledgements

The authors would like to thank Carlo Gasbarri for many inspiring discussions on this topic.

References

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    Atiyah M F, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957) 181–207Google Scholar
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    Biswas I, A criterion for flatness of sections of adjoint bundle of a holomorphic principal bundle over a Riemann surface, Documenta Math. (to appear)Google Scholar
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    Biswas I and Heu V, Holomorphic connections on filtered bundles over curves, preprintGoogle Scholar
  4. [4]
    Biswas I and Heu V, Holomorphic connections on filtered bundles with given connection on the graded bundle, preprintGoogle Scholar
  5. [5]
    Esnault H and Viehweg E, Semistable bundles on curves and irreducible representations of the fundamental group. Algebraic geometry: Hirzebruch 70 (Warsaw, 1998), 129–138, Contemp. Math., 241, Amer. Math. Soc., Providence, RI 1999Google Scholar
  6. [6]
    Weil A, Généralisation des fonctions abéliennes, Jour. Math. Pure Appl. 17 (1938) 47–87Google Scholar

Copyright information

© Indian Academy of Sciences 2014

Authors and Affiliations

  1. 1.School of MathematicsTata Institute of Fundamental ResearchBombayIndia
  2. 2.Institut de Recherche Mathématique AvancéeStrasbourg CedexFrance

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