Geodesic
Pathological MMP singularities as αp-quotients
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e185

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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. 
Posva, Quentin. Pathological MMP singularities as αp-quotients. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e185. doi: 10.1017/fms.2025.10129
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