The prym map on divisors, and the slope of A₅

In this paper, we compute the pullbacks of divisor classes from the perfect cone compactification of the moduli space of abelian varieties to the Deligne-Mumford compactification of the moduli space of curves under the Prym map (extended to the boundary). As an application, we obtain a bound on the slope of the effective cone of the moduli space of abelian five-folds. In the appendix by Klaus Hulek, the notion of slope for arbitrary toroidal compactifications is discussed, and the slope bound is shown to hold in general.