Donaldson-Thomas invariants of $[{\mathbb{C}}^4\mathrm{/}{\mathbb{Z}}_r]$

We compute the zero-dimensional Donaldson-Thomas invariants of the quotient stack $[{\mathbb{C}}^4\mathrm{/}{\mathbb{Z}}_r]$, confirming a conjecture of Cao-Kool-Monavari. Our main theorem is established through an orbifold analogue of Cao-Zhao-Zhou’s degeneration formula combined with the zero-dimensional Donaldson-Thomas invariants for ${\mathcal{A}}_{r-1}\times {\mathbb{C}}^2$ and an explicit determination of orientations of Hilbert schemes of points on $[{\mathbb{C}}^4\mathrm{/}{\mathbb{Z}}_r]$.