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arXiv · 2501.01179

Pathological MMP singularities as $\alpha_p$-quotients

Quentin Posva
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Abstract

We construct pathological examples of MMP singularities in every positive characteristic using quotients by $\alpha_p$-actions. In particular, we obtain non-$S_3$ terminal singularities, as well as locally stable (respectively stable) families whose general fibers are smooth (respectively klt, Cohen--Macaulay and $F$-injective) and whose special fibers are non-$S_2$. The dimensions of these examples are bounded below by a linear function of the characteristic.

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Quentin Posva. 2025-01-02. Pathological MMP singularities as $\alpha_p$-quotients. https://arxiv.org/abs/2501.01179

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