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

Masayuki Hirokado

Published 2016-07-28Version 1

We continue to study and present concrete examples in characteristic 2 of compound Du Val singularities defined over an algebraically closed field which have one dimensional singular loci but cannot be written as products (a rational double point) x (a curve) up to analytic isomorphism at any point of the loci. Unlike in other characteristics, we find a large number of such examples whose general hyperplane sections have rational double points of type D. We consider these compound Du Val singularities as a special class of canonical singularities, intend to complete classification in arbitrary characteristic reinforcing Miles Reid's result in characteristic zero.