Ciliberto, Ciro; van der Geer, Gerard

Andreotti-Mayer loci and the Schottky problem

Doc. Math., J. DMV 13, 453-504 (2008)

Summary

Summary: 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 ${\Acal}_g$ 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.

Mathematics Subject Classification

14K10

Keywords/Phrases

abelian variety, theta divisor, andreotti-Mayer loci, Schottky problem

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