The Euler characteristic of $\mathcal A_g$ via Hodge integrals

TL;DR

This paper proves the Harder-Siegel formula for the Euler characteristic of the moduli space of abelian varieties using intersection theory and recent vanishing results for lambda classes on compactifications.

Contribution

It establishes the Harder-Siegel formula for $\

Findings

Proof of the Harder-Siegel formula for $\

Application of vanishing results for lambda classes on boundary of compactifications

Connection between intersection theory and Euler characteristic computation

Abstract

We prove the Harder-Siegel formula for the Euler characteristic of $\mathcal{A}_g$ via the intersection theory of $\overline{\mathcal{M}}_g$ and a vanishing result for lambda classes on the boundary of the toroidal compactifications of $\mathcal{A}_g$, recently proven by Canning, Molcho, Oprea and Pandharipande.