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Equations of genus $4$ curves from their theta constants

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arxiv 2402.03160 v4 pith:OJ3VGXK6 submitted 2024-02-05 math.AG math.NT

Jeroen Hanselman , Andreas Pieper , Sam Schiavone This is my paper · ORCID
classification math.AGmath.NT
keywords constantsequationsgenusthetaaroundarticlebeautifulclassical
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abstract

In this article we give explicit formulas for the equations of a generic genus $4$ curve in terms of its theta constants. The method uses the Prym construction and the beautiful classical geometry around it.

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Cited by 1 Pith paper

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  1. The Torelli locus and Newton polygons

    math.AG 2025-08 conditional novelty 3.0 of 10

    A survey of the Torelli locus and Newton polygons that corrects a previously erroneous genus computation and thereby proves new infinite families of supersingular curves of genus δp(p−1)/2.

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