Characterizing Jacobians via the KP equation and via flexes and degenerate trisecants to the Kummer variety: An algebro-geometric approach

Enrico Arbarello, Giulio Codogni, Giuseppe Pareschi

Research output: Contribution to journalArticlepeer-review

Abstract

We give completely algebro-geometric proofs of a theorem by T. Shiota, and of a theorem by I. Krichever, characterizing Jacobians of algebraic curves among all irreducible principally polarized abelian varieties. Shiota's characterization is given in terms of the KP equation. Krichever's characterization is given in terms of trisecant lines to the Kummer variety. Here we treat the case of flexes and degenerate trisecants. The basic tool we use is a theorem we prove asserting that the base locus of the linear system associated to an effective line bundle on an abelian variety is reduced. This result allows us to remove all the extra assumptions that were introduced in the theorems by the first author, C. De Concini, G.Marini, and O. Debarre, in order to achieve algebro-geometric proofs of the results above.

Original languageEnglish
Pages (from-to)251-271
Number of pages21
JournalJournal fur die Reine und Angewandte Mathematik
Volume2021
Issue number777
DOIs
Publication statusPublished - 1 Aug 2021
Externally publishedYes

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