Andreotti-Mayer loci and the Schottky problem

2007/01/12 by Ciro Ciliberto, Gerard van der Geer, Ciliberto, Ciro +1
Biochemistry, Genetics and Molecular Biology · Chemistry · #Algebraic Geometry (math.AG) #Crystal structures of chemical compounds #FOS: Mathematics #Microtubule and mitosis dynamics

paper · pdf · doi:10.48550/arxiv.math/0701353

openalex publication_date 2007/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove a lower bound for the codimension of the Andreotti-Mayer locus N_g,1 and show that the lower bound is reached only for the hyperelliptic locus in genus 4 and the Jacobian locus in genus 5. In relation with the boundary of the Andreotti-Mayer loci we study subvarieties of principally polarized abelian varieties (B,Theta) parametrizing points b such that Theta and the translate Theta_b are tangentially degenerate along a variety of a given dimension.

Citations

• The Moduli Space of Abelian Varieties and the Singularities of the Theta Divisor

Related

• Prym loci of branched double coverings and generalized Andreotti-Mayer loci
• The Moduli Space of Abelian Varieties and the Singularities of the Theta Divisor
• Degeneracy loci in the universal family of Abelian varieties
• The degree of the Jacobian locus and the Schottky problem
• Degeneracy loci in the universal family of abelian varieties