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Torsion-free sheaves on nodal curves and triples

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Abstract

Let X be a reduced irreducible curve with at most nodes as singularities with normalization π: \( \tilde X \) → X. We study the description of torsion free sheaves on X in terms of vector bundles with an additional structure on \( \tilde X \) which was introduced by Seshadri.

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References

  1. U.N. Bhosle. Generalized parabolic bundles and applications to torsionfree sheaves on nodal curves. Ark. Mat., 30 (1992), 187–215.

    Article  MATH  MathSciNet  Google Scholar 

  2. U.N. Bhosle. Maximal subsheaves of torsion-free sheaves on nodal curves. Journ. London Math. Soc., 74 (2006), 59–74.

    Article  MATH  MathSciNet  Google Scholar 

  3. I. Burban and Y. Drozd. Coherent sheaves on rational curves with simple double points and transversal intersections. Duke Math. J., 121 (2004), 189–229.

    Article  MATH  MathSciNet  Google Scholar 

  4. I. Burban, Y. Drozd and G.-M. Greuel. Vector bundles on singular projective curves. Kluwer Acad. Publ., NATO Sci. Ser. II, Math. Phys. Chem., 36 (2001), 1–15.

    MathSciNet  Google Scholar 

  5. A. Grothendieck. Sur quelques points d’algèbre homologique. Tohoku Math. J., 9 (1957), 119–221.

    MATH  MathSciNet  Google Scholar 

  6. A. Hirschowitz. Problème de Brill-Noether en rang supérieur. Preprint 91, Université de Nice (1986).

  7. H. Lange. Zur Klassifikation von Regelmannigfaltigkeiten. Math. Ann., 262 (1083), 447–459

    Article  Google Scholar 

  8. S. Mukai and F. Sakai. Maximal subbundles of vector bundles on a curve. Manuscr. Math., 52 (1985), 251–256.

    Article  MATH  MathSciNet  Google Scholar 

  9. M.S. Narasimhan and S. Ramanan. Deformations of the moduli space of vector bundles over an algebraic curve. Ann. of Math., 101 (1975), 391–417.

    Article  MathSciNet  Google Scholar 

  10. C.S. Seshadri. Fibrés vectoriels sur les courbes algébriques. Astérisque, 96 (1982).

  11. S. Sundaram. Special divisors and vector bundles. Tohoku Math. J., 39 (1987), 175–213.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Minas Gerais, Av. Antonio Carlos 6627, 30161-970, Belo Horizonte, MG, Brazil

    D. Avritzer

  2. Mathematisches Institut, Universität Erlangen-Nüremberg, Bismarckstrasse 1 1/2, 91054, Erlangen, Germany

    H. Lange

  3. Departamento de Matemática, Universidade Federal de Juiz de Fora ICE Campus Universitario, B. Martelos, 36036-330, Juiz de Fora, MG, Brazil

    F. A. Ribeiro

Authors
  1. D. Avritzer
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  2. H. Lange
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  3. F. A. Ribeiro
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Corresponding author

Correspondence to D. Avritzer.

Additional information

Partially supported by CNPq-Grant 301618/2008-9, DAAD-FAPEMIG.

Partially supported by DAAD-FAPEMIG cooperation agreement.

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Avritzer, D., Lange, H. & Ribeiro, F.A. Torsion-free sheaves on nodal curves and triples. Bull Braz Math Soc, New Series 41, 421–447 (2010). https://doi.org/10.1007/s00574-010-0020-1

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  • DOI: https://doi.org/10.1007/s00574-010-0020-1

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