On the universal abelian variety of dimension 4

TL;DR

This paper proves that the universal abelian variety of dimension 4 and its universal theta divisor are unirational, providing insights into their geometric structure over algebraically closed fields.

Contribution

It establishes the unirationality of the universal abelian variety and theta divisor of dimension 4, a significant result in algebraic geometry.

Findings

Universal abelian variety of dimension 4 is unirational.

Universal theta divisor over the moduli space is unirational.

Results hold over algebraically closed fields with characteristic not 2 or 3.

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.