Purely Log Terminal Threefolds with Non-Normal Centres in Characteristic Two

We show that many classical results of the minimal model program 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.