JournalsprimsVol. 40, No. 4pp. 1241–1265

Compactified Jacobians and Torelli Map

  • Valery Alexeev

    University of Georgia, Athens, United States
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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.

Cite this article

Valery Alexeev, Compactified Jacobians and Torelli Map. Publ. Res. Inst. Math. Sci. 40 (2004), no. 4, pp. 1241–1265

DOI 10.2977/PRIMS/1145475446