Vector bundles and torsion free sheaves on degenerations of elliptic curves

Details Vector bundles and torsion free sheaves on degenerations of elliptic curves Vector bundles and torsion free sheaves on degenerations of elliptic curves

2006-03-12

arxiv.org/abs/math/0603261v2

Mathematics

Algebraic Geometry

39 pages, 5 figures

Scientific paper

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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