# Singularities of theta divisors and the geometry of ${\mathcal{A}}_{5}$

Gavril Farkas; Samuele Grushevsky; Salvati R. Manni; Alessandro Verra

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 9, page 1817-1848
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topFarkas, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.