Purely log terminal threefolds with non-normal centres in characteristic two

TL;DR

This paper demonstrates that many classical minimal model program results fail in characteristic two, providing explicit counterexamples involving non-normal centers, non-rational singularities, and non-trivial cohomology.

Contribution

It constructs explicit threefold examples showing the failure of classical results in characteristic two, highlighting new phenomena in positive characteristic algebraic geometry.

Findings

Counterexamples to minimal model program results in characteristic two

Existence of non-normal centers in threefold plt pairs

Presence of non-rational, non-Cohen-Macaulay klt singularities

Abstract

We show that many classical results of the minimal model programme do not hold over an algebraically closed field of characteristic two. Indeed, we construct a three dimensional plt pair whose codimension one part is not normal, a three dimensional klt singularity which is not rational nor Cohen-Macaulay, and a klt Fano threefold with non-trivial intermediate cohomology.