The universal abelian variety of dimension five and the geometry of A_6

It is well-known that the boundary divisor of the moduli space A_g of principally polarized abelian varieties of dimension g is isomorphic to the universal Kummer variety in dimension g-1. I will discuss joint work with Verra, in which we establish a structure result for the universal abelian five-fold in terms of discriminant curves of conic bundles over a del Pezzo surface. This gives a very simple unirational parametrization of the boundary divisor of A_6 and a lower bound for the slope of this moduli space.