An explicit solution to the weak Schottky problem

Hershel M. Farkas; Samuel Grushevsky; Riccardo Salvati Manni

doi:10.14231/AG-2021-009

An explicit solution to the weak Schottky problem

Hershel M. Farkas^*, Samuel Grushevsky, Riccardo Salvati Manni

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We give an explicit weak solution to the Schottky problem, in the spirit of Riemann and Schottky. For any genus g, we write down a collection of polynomials in genus g theta constants such that their common zero locus contains the locus of Jacobians of genus g curves as an irreducible component. These polynomials arise by applying a specific Schottky–Jung proportionality to an explicit collection of quartic identities for genus g - 1 theta constants.

Original language	English
Pages (from-to)	358-373
Number of pages	16
Journal	Algebraic Geometry
Volume	8
Issue number	3
DOIs	https://doi.org/10.14231/AG-2021-009
State	Published - 2021

Bibliographical note

Publisher Copyright:
© 2020. Foundation Compositio Mathematica 2021. This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse, distribution, and reproduction in any medium, provided that the original work is properly cited. For commercial re-use, please contact the Foundation Compositio Mathematica. All Rights Reserved.

Keywords

Schottky problem
theta function

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10.14231/AG-2021-009

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AU - Manni, Riccardo Salvati

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PY - 2021

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N2 - We give an explicit weak solution to the Schottky problem, in the spirit of Riemann and Schottky. For any genus g, we write down a collection of polynomials in genus g theta constants such that their common zero locus contains the locus of Jacobians of genus g curves as an irreducible component. These polynomials arise by applying a specific Schottky–Jung proportionality to an explicit collection of quartic identities for genus g - 1 theta constants.

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An explicit solution to the weak Schottky problem

Abstract

Bibliographical note

Keywords

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