Pathological MMP singularities as αp-quotients
Abstract
We construct pathological examples of MMP singularities in every positive characteristic using quotients by αp-actions. In particular, we obtain non-S3 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-S2. The dimensions of these examples are bounded below by a linear function of the characteristic.
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