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Vector Bundles and Torsion Free Sheaves on Degenerations of Elliptic Curves

In: Global Aspects of Complex Geometry

Author

Listed:
  • Lesya Bodnarchuk

    (Technische Universität Kaiserslautern)

  • Igor Burban

    (Johannes Gutenberg-Universität Mainz, Institut für Mathematik)

  • Yuriy Drozd

    (Kyiv Taras Shevchenko University, Department of Mechanics and Mathematics)

  • Gert-Martin Greuel

    (Technische Universität Kaiserslautern)

Abstract

Summary In this paper we give a survey about the classification of vector bundles and torsion free sheaves on degenerations of elliptic curves. Coherent sheaves on singular curves of arithmetic genus one can be studied using the technique of matrix problems or via Fourier-Mukai transforms, both methods are discussed here. Moreover, we include new proofs of some classical results about vector bundles on elliptic curves.

Suggested Citation

  • Lesya Bodnarchuk & Igor Burban & Yuriy Drozd & Gert-Martin Greuel, 2006. "Vector Bundles and Torsion Free Sheaves on Degenerations of Elliptic Curves," Springer Books, in: Fabrizio Catanese & Hélène Esnault & Alan T. Huckleberry & Klaus Hulek & Thomas Peternell (ed.), Global Aspects of Complex Geometry, pages 83-128, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-35480-2_3
    DOI: 10.1007/3-540-35480-8_3
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