Geodesic
Singularities of theta divisors and the geometry of $\mathcal A_5$
Journal of the European Mathematical Society, Tome 16 (2014) no. 9, pp. 1817-1848.

Voir la notice de l'article provenant de la source EMS Press

We study the codimension two locus H in Ag​ consisting of principally polarized abelian varieties whose theta divisor has a singularity that is not an ordinary double point. We compute the class [H]∈CH2(Ag​) for every g. For g=4, this turns out to be the locus of Jacobians with a vanishing theta-null. For g=5, via the Prym map we show that H⊂A5​ has two components, both unirational, which we describe completely. We then determine the slope of the effective cone of A5​​ and show that the component N0′​​ of the Andreotti-Mayer divisor has minimal slope and the Iitaka dimension κ(A5​​,N0′​​) is equal to zero.
DOI : 10.4171/jems/476
Classification : 14-XX, 00-XX
Keywords: Theta divisor, moduli space of principally polarized abelian varieties, effective cone, Prym variety 
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     title = {Singularities of theta divisors and the geometry of $\mathcal A_5$},
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Gavril Farkas; Samuel Grushevsky; R. Salvati Manni; Alessandro Verra. Singularities of theta divisors and the geometry of $\mathcal A_5$. Journal of the European Mathematical Society, Tome 16 (2014) no. 9, pp. 1817-1848. doi : 10.4171/jems/476. http://geodesic.mathdoc.fr/articles/10.4171/jems/476/

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