An explicit solution to the weak Schottky problem

Hershel Farkas; Samuel Grushevsky; Riccardo Salvati Manni

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arXiv · 1710.02938

An explicit solution to the weak Schottky problem

Hershel Farkas·Samuel Grushevsky·Riccardo Salvati Manni

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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 theta constants in genus $g-1$, which are suitable linear combinations of Riemann's quartic relations.

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Hershel Farkas, Samuel Grushevsky, Riccardo Salvati Manni. 2020-10-12. An explicit solution to the weak Schottky problem. https://arxiv.org/abs/1710.02938

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