Andreotti-Mayer loci and the Schottky problem

Details Andreotti-Mayer loci and the Schottky problem Andreotti-Mayer loci and the Schottky problem

2007-01-12

arxiv.org/abs/math/0701353v1

Mathematics

Algebraic Geometry

46 pages, Latex

Scientific paper

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.

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