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

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 $[K^nX/X_n]$.