Classification of threefold canonical thresholds

Jheng-Jie Chen; Jiun-Cheng Chen; Hung-Yi Wu

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arXiv · 2411.12373

Classification of threefold canonical thresholds

Jheng-Jie Chen·Jiun-Cheng Chen·Hung-Yi Wu

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Abstract

We show that the set $\mathcal{T}_{3, \mathrm{sm}}^{\mathrm{can}}$ of smooth threefold canonical thresholds coincides with $\mathcal{T}_{2, \mathrm{sm}}^{\mathrm{lc}}=\mathcal{HT}_{2}$, where $\mathcal{HT}_{2}$ is the $2$-dimensional hypersurface log canonical thresholds characterized by Kuwata \cite{K99a, K99b}. We classify the set $\mathcal{T}_{3}^{\mathrm{can}}$ of threefold canonical thresholds. More precisely, we prove $\mathcal{T}_{3}^{\mathrm{can}}= \{0\} \cup \{\frac{4}{5}\} \cup \mathcal{T}_{3, \mathrm{sm}}^{\mathrm{can}}$.

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Jheng-Jie Chen, Jiun-Cheng Chen, Hung-Yi Wu. 2024-11-19. Classification of threefold canonical thresholds. https://arxiv.org/abs/2411.12373

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