Canonical singularities of dimension three in characteristic 2 which do not follow Reid’s rules

Abstract

We continue studying compound Du Val singularities defined over an algebraically closed field $k$, and present concrete examples in characteristic $2$ which have one-dimensional singular loci but do not admit a description as a trivial product (a rational double point) $\times$ (a curve) up to analytic isomorphism at any point. Unlike in other characteristics, we find a large number of such examples whose general hyperplane sections have rational double points of type $D$. These compound Du Val singularities shall be viewed as a special class of canonical singularities. In the previous work with Ito and Saito, we classified such singularities in $p\ge 3$,

and I intend to complete our classification in arbitrary characteristic, reinforcing Reid’s result in characteristic $0$.