- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:10
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
16
2014
9
Singularities of theta divisors and the geometry of $\mathcal A_5$
Gavril
Farkas
Humboldt-Universität zu Berlin, BERLIN, GERMANY
Samuele
Grushevsky
Stony Brook University, STONY BROOK, UNITED STATES
R.
Salvati Manni
Università di Roma La Sapienza, ROMA, ITALY
Alessandro
Verra
Università degli studi Roma Tre, ROMA, ITALY
Theta divisor, moduli space of principally polarized abelian varieties, effective cone, Prym variety
We study the codimension two locus $H$ in $\mathcal A_g$ consisting of principally polarized abelian varieties whose theta divisor has a singularity that is not an ordinary double point. We compute the class $[H]\in CH^2(\mathcal A_g)$ 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 $H\subset \mathcal A_5$ has two components, both unirational, which we describe completely. We then determine the slope of the effective cone of $\overline{\mathcal A_5}$ and show that the component $\overline{N_0'}$ of the Andreotti-Mayer divisor has minimal slope and the Iitaka dimension $\kappa(\overline{\mathcal A_5}, \overline{N_0'})$ is equal to zero.
Algebraic geometry
General
1817
1848
10.4171/JEMS/476
http://www.ems-ph.org/doi/10.4171/JEMS/476