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 intersection of the Andreotti-Mayer loci with the boundary of the moduli space {\mathcal A}_g we study subvarieties of principally polarized abelian varieties (B,\Xi) parametrizing points b such that \Xi and the translate \Xi_b are tangentially degenerate along a variety of a given dimension.
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