Vector Bundles and Torsion Free Sheaves on Degenerations of Elliptic Curves

Lesya Bodnarchuk (), Igor Burban (), Yuriy Drozd () and Gert-Martin Greuel ()
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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

A chapter in Global Aspects of Complex Geometry, 2006, pp 83-128 from Springer

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.

Keywords: Vector Bundle; Line Bundle; Elliptic Curve; Elliptic Curf; Projective Line (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-35480-2_3

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DOI: 10.1007/3-540-35480-8_3

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