Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstrass cubics

Details Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstrass cubics Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstrass cubics

2004-01-30

arxiv.org/abs/math/0401437v3

Mathematics

Algebraic Geometry

minor changes; to appear in J. Reine Angew. Math.; 42 pages

Scientific paper

We completely describe all semi-stable torsion free sheaves of degree zero on nodal cubic curves using the technique of Fourier-Mukai transforms. The Fourier-Mukai images of such sheaves are torsion sheaves of finite length, which we compute explicitly. We show how to obtain an SL(2,Z)-action (up to shifts) on the bounded derived category of coherent sheaves on any Weierstass cubic.

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