Vector bundles and torsion free sheaves on degenerations of elliptic curves

2006/03/12 by Lesya Bodnarchuk, Igor Burban, Bodnarchuk, Lesya +5
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0603261

39 pages, 5 figures

arxiv created 2006/06/12 · arxiv updated 2009/12/01

Abstract

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.

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