Some intersection numbers of divisors on toroidal compactifications of A_g

TL;DR

This paper computes specific intersection numbers of boundary and Hodge divisors on toroidal compactifications of the moduli space of principally polarized abelian varieties, focusing on those away from a particular boundary stratum.

Contribution

It provides explicit calculations of intersection numbers on toroidal compactifications, advancing understanding of the geometry of $A_g$ and its boundary components.

Findings

Computed top intersection numbers of boundary and Hodge divisors.

Identified intersection numbers away from the stratum over $A_{g-3}$.

Enhanced understanding of the boundary geometry of $A_g$.

Abstract

We study the top intersection numbers of the boundary and Hodge class divisors on toroidal compactifications of the moduli space $A_g$ of principally polarized abelian varieties and compute those numbers that live away from the stratum which lies over the closure of $A_{g-3}$ in the Satake compactification.