On the universal abelian variety of dimension 4

Abstract

Let A be the moduli space of principally polarized abelian varieties of dimension 4 over an algebraically closed field k of characteristic different from 2,3. It is proved that the universal principally polarized abelian variety over A, as well as the universal theta divisor over A, are unirational varieties.

Referee's version, appearing on Contemporary Math. vol. 465 (2008)