JournalsprimsVol. 40 , No. 4DOI 10.2977/prims/1145475446

Compactified Jacobians and Torelli Map

  • Valery Alexeev

    University of Georgia, Athens, United States
Compactified Jacobians and Torelli Map cover

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.