Heegner divisors in the moduli space of genus three curves

2005/10/10 by Michela Artebani, Artebani, Michela
Mathematics · #14H10 #14J10 #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #math.AG #msc:14H10 #msc:14J10 #msc:14J28

paper · pdf · doi:10.48550/arxiv.math/0510199

arxiv created 2005/10/10 · openalex publication_date 2005/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

S. Kondō used periods of K3 surfaces to prove that the moduli space of genus three curves is birational to an arithmetic quotient of a complex 6-ball. In this paper we study Heegner divisors in the ball quotient, given by arithmetically defined hyperplane sections of the ball. We show that the corresponding loci of genus three curves are given by: hyperelliptic curves, singular plane quartics and plane quartics admitting certain rational "splitting curves".

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