Pathological MMP Singularities from Alpha-p Quotients in Positive Characteristic
In positive characteristic p, quotients of affine space by alpha_p group-scheme actions (equivalently, quotients by rank-one 1-foliations from a p-nilpotent derivation) produce Minimal Model Program singularities with pathological cohomological behavior absent in characteristic zero: isolated canonical and terminal singularities that fail Serre's condition S3, and locally stable families whose special fibers are non-S2. These constructions bound the failure of the KSBA moduli theory of stable pairs to compactify properly.
PATHOLOGICAL MMP SINGULARITIES AS αp-QUOTIENTS QUENTIN POSVA Abstract. We construct pathological
Constructs new pathological singularities of the Minimal Model Program in every positive characteristic p by taking quotients of affine space by alpha_p-actions, studied through the lens of rank-one …