Donaldson-Thomas invariants of $[\mathbb C^4/\mathbb Z_r]$

Xiaolong Liu

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arXiv · 2507.21582

Donaldson-Thomas invariants of $[\mathbb C^4/\mathbb Z_r]$

Xiaolong Liu

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Abstract

We compute the zero-dimensional Donaldson-Thomas invariants of the quotient stack $[\mathbb{C}^4/\mathbb{Z}_r]$, 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 $\widetilde{\mathbb C^2/\mathbb Z_r}\times\mathbb{C}^2$ and an explicit determination of orientations of Hilbert schemes of points on $[\mathbb{C}^4/\mathbb{Z}_r]$.

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Xiaolong Liu. 2025-07-29. Donaldson-Thomas invariants of $[\mathbb C^4/\mathbb Z_r]$. https://arxiv.org/abs/2507.21582

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