An explicit solution to the weak Schottky problem

2017/10/09 by Farkas, Hershel, Grushevsky, Samuel, Manni, Riccardo Salvati
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1710.02938

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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