The Euler characteristic of the generalized Kummer scheme of an Abelian threefold

TL;DR

This paper derives a formula linking the Euler characteristic of generalized Kummer schemes of an Abelian threefold to plane partitions, providing a key computation for Donaldson-Thomas invariants.

Contribution

It proves a conjectured formula connecting Euler characteristics of Kummer schemes to combinatorial plane partitions, advancing understanding of Donaldson-Thomas invariants.

Findings

Established a formula for Euler characteristics of Kummer schemes

Connected geometric invariants to combinatorial plane partitions

Computed Donaldson-Thomas invariants for specific moduli stacks

Abstract

Let $X$ be an Abelian threefold. We prove a formula, conjectured by the first author, expressing the Euler characteristic of the generalized Kummer schemes $K^nX$ of $X$ in terms of the number of plane partitions. This computes the Donaldson-Thomas invariant of the moduli stack $[K^nX/X_n]$.