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.