The Prym map on divisors, and the slope of A_5

TL;DR

This paper computes divisor class pullbacks under the Prym map to establish a lower bound on the slope of effective divisors on the moduli space of abelian fivefolds, with implications for various compactifications.

Contribution

It provides the first calculation of the Prym map's effect on divisor classes extended to the boundary, leading to new slope bounds for abelian fivefold moduli spaces.

Findings

Lower bound on the slope of effective divisors on A_5

Extension of the Prym map to boundary divisors

Slope bound applies to general toroidal compactifications

Abstract

In this paper we compute the pullback of divisor classes under the Prym map (extended to the boundary), and apply this result to get a lower bound on the slope of effective divisors on the perfect cone compactification of the moduli space of principally polarized abelian fivefolds. 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.