Compactified jacobians and Torelli map

We compare several constructions of compactified jacobians - using semistable sheaves, semistable projective curves, degenerations of abelian varieties, and combinatorics of cell decompositions - and show that they are equivalent. We give a detailed description of the "canonical compactified jacobian" in degree g - 1. Finally, we explain how Kapranov's compactification of configuration spaces can be understood as a toric analog of the extended Torelli map.