Singularities of theta divisors and the geometry of ${𝒜}_5$

Farkas, Gavril, et al. "Singularities of theta divisors and the geometry of $\mathcal {A}_5$." Journal of the European Mathematical Society 016.9 (2014): 1817-1848. <http://eudml.org/doc/277380>.

@article{Farkas2014,
abstract = {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 $\overline\{N_0^\{\prime \}\}$ of the Andreotti-Mayer divisor has minimal slope and the Iitaka dimension $\kappa (\overline\{\mathcal \{A\}_5\}, \overline\{N_0^\{\prime \}\})$ is equal to zero.},
author = {Farkas, Gavril, Grushevsky, Samuele, Manni, Salvati R., Verra, Alessandro},
journal = {Journal of the European Mathematical Society},
keywords = {theta divisor; moduli space of principally polarized abelian varieties; effective cone; Prym variety; theta divisor; moduli space of principally polarized abelian varieties; effective cone; Prym variety},
language = {eng},
number = {9},
pages = {1817-1848},
publisher = {European Mathematical Society Publishing House},
title = {Singularities of theta divisors and the geometry of $\mathcal \{A\}_5$},
url = {http://eudml.org/doc/277380},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Farkas, Gavril
AU - Grushevsky, Samuele
AU - Manni, Salvati R.
AU - Verra, Alessandro
TI - Singularities of theta divisors and the geometry of $\mathcal {A}_5$
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 9
SP - 1817
EP - 1848
AB - 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 $\overline{N_0^{\prime }}$ of the Andreotti-Mayer divisor has minimal slope and the Iitaka dimension $\kappa (\overline{\mathcal {A}_5}, \overline{N_0^{\prime }})$ is equal to zero.
LA - eng
KW - theta divisor; moduli space of principally polarized abelian varieties; effective cone; Prym variety; theta divisor; moduli space of principally polarized abelian varieties; effective cone; Prym variety
UR - http://eudml.org/doc/277380
ER -