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

Igor Burban·Bernd Kreussler
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Abstract

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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Igor Burban, Bernd Kreussler. 2004-10-15. Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstrass cubics. https://arxiv.org/abs/math/0401437

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