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.
Cite this article
Valery Alexeev, Compactiﬁed Jacobians and Torelli Map. Publ. Res. Inst. Math. Sci. 40 (2004), no. 4, pp. 1241–1265DOI 10.2977/PRIMS/1145475446