The Euler characteristic of the generalized Kummer scheme of an abelian threefold (Q292049)

The authors prove that the Euler characteristic of the generalized Kummer scheme of an abelian threefold is given by \[ \chi(K^n X)= n^5\sum_{d|n}d^2. \] This formula allows them to show that the Donaldson-Thomas invariant of the moduli stack \([K^n X / X_n]\) is equal to \(\displaystyle\frac{(-1)^{n+1}}{n}\sum_{d|n}d^2\).