Geodesic
Andreotti-Mayer loci and the Schottky problem
Documenta mathematica, Tome 13 (2008), pp. 453-504
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We prove a lower bound for the codimension of the Andreotti-Mayer locus Ng,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 Ag​ we study subvarieties of principally polarized abelian varieties (B,Ξ) parametrizing points b such that Ξ and the translate Ξb​ are tangentially degenerate along a variety of a given dimension.
DOI : 10.4171/dm/252
Classification : 14K10
Mots-clés : abelian variety, theta divisor, andreotti-Mayer loci, Schottky problem 
@article{10_4171_dm_252,
     author = {Ciro Ciliberto and Gerard van der Geer},
     title = {Andreotti-Mayer loci and the {Schottky} problem},
     journal = {Documenta mathematica},
     pages = {453--504},
     year = {2008},
     volume = {13},
     doi = {10.4171/dm/252},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/252/}
}
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Ciro Ciliberto; Gerard van der Geer. Andreotti-Mayer loci and the Schottky problem. Documenta mathematica, Tome 13 (2008), pp. 453-504. doi: 10.4171/dm/252

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