On the Schottky problem for genus five Jacobians with a vanishing theta null
| Autor: | Daniele Agostini, Lynn Chua |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Abelian variety
Pure mathematics Quadric Gauss map Mathematics - Complex Variables Schottky problem 010102 general mathematics Tangent cone Null (mathematics) Theta divisor 01 natural sciences Theoretical Computer Science 14K10 14K25 14H40 14H42 14Q99 010101 applied mathematics Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Mathematics (miscellaneous) Genus (mathematics) FOS: Mathematics Complex Variables (math.CV) 0101 mathematics Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. :333-350 |
| ISSN: | 2036-2145 0391-173X |
| DOI: | 10.2422/2036-2145.201909_013 |
| Popis: | We give a solution to the weak Schottky problem for genus five Jacobians with a vanishing theta null, answering a question of Grushevsky and Salvati Manni. More precisely, we show that if a principally polarized abelian variety of dimension five has a vanishing theta null with a quadric tangent cone of rank at most three, then it is in the Jacobian locus, up to extra irreducible components. We employ a degeneration argument, together with a study of the ramification loci for the Gauss map of a theta divisor. Comment: 18 pages, comments very welcome |
| Databáze: | OpenAIRE |
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