Abstract
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.
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