Pathological MMP singularities as $\hat{I}{\pm }_p$-quotients

Abstract

We construct pathological examples of MMP singularities in every positive characteristic using quotients by $\hat{I}{\pm }_p$-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.

v2: 27 pages, comments welcome anytime. Some results have been improved, some minor mistakes have been corrected