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

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 .nite length, which we compute explicitly. We show that the twist functors, which are associated to the structure sheaf O and the structure sheaf k(p₀) of a smooth point p₀, generate an SL(2,ℤ)-action (up to shifts) on the bounded derived category of coherent sheaves on any Weierstraß cubic.