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 
@article{JEMS_2014_16_9_a1,
     author = {Gavril Farkas and Samuel Grushevsky and R. Salvati Manni and Alessandro Verra},
     title = {Singularities of theta divisors and the geometry of $\mathcal A_5$},
     journal = {Journal of the European Mathematical Society},
     pages = {1817--1848},
     publisher = {mathdoc},
     volume = {16},
     number = {9},
     year = {2014},
     doi = {10.4171/jems/476},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/476/}
}
TY  - JOUR
AU  - Gavril Farkas
AU  - Samuel Grushevsky
AU  - R. Salvati Manni
AU  - Alessandro Verra
TI  - Singularities of theta divisors and the geometry of $\mathcal A_5$
JO  - Journal of the European Mathematical Society
PY  - 2014
SP  - 1817
EP  - 1848
VL  - 16
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/476/
DO  - 10.4171/jems/476
ID  - JEMS_2014_16_9_a1
ER  - 
%0 Journal Article
%A Gavril Farkas
%A Samuel Grushevsky
%A R. Salvati Manni
%A Alessandro Verra
%T Singularities of theta divisors and the geometry of $\mathcal A_5$
%J Journal of the European Mathematical Society
%D 2014
%P 1817-1848
%V 16
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/476/
%R 10.4171/jems/476
%F JEMS_2014_16_9_a1
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

Cité par Sources :