Characterizing Jacobians via the KP equation and via flexes and degenerate trisecants to the Kummer variety: an algebro-geometric approach
| Autor: | Giuseppe Pareschi, Enrico Arbarello, Giulio Codogni |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Abelian variety
Pure mathematics Applied Mathematics General Mathematics Jacobians 010102 general mathematics Degenerate energy levels Kadomtsev–Petviashvili equation 01 natural sciences Base locus Settore MAT/03 Mathematics - Algebraic Geometry Nonlinear Sciences::Exactly Solvable and Integrable Systems Mathematics::Algebraic Geometry Line bundle 0103 physical sciences FOS: Mathematics 14H42 (Primary) 37K10 14K12 (Secondary) 010307 mathematical physics Algebraic curve 0101 mathematics Variety (universal algebra) Abelian group Algebraic Geometry (math.AG) Mathematics |
| Popis: | 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. Comment: 21 pages. Minor changes. To appear in Crelle's Journal |
| Databáze: | OpenAIRE |
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