We continue studying compound Du Val singularities defined over an algebraically closed field , and present concrete examples in characteristic which have one-dimensional singular loci but do not admit a description as a trivial product (a rational double point) (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 . 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 ,
and I intend to complete our classification in arbitrary characteristic, reinforcing Reid’s result in characteristic .
"Canonical singularities of dimension three in characteristic which do not follow Reid’s rules." Kyoto J. Math. 59 (4) 747 - 768, December 2019. https://doi.org/10.1215/21562261-2019-0026