INSEPARABLE MAPS ON Wn-VALUED LOCAL COHOMOLOGY GROUPS OF NONTAUT RATIONAL DOUBLE POINT SINGULARITIES AND THE HEIGHT OF K3 SURFACES

Abstract

We consider rational double point singularities (RDPs) that are nontaut, which means that the isomorphism class is not uniquely determined from the dual graph of the minimal resolution. Such RDPs exist in characteristic $2,3$, and $5$. We compute the actions of Frobenius and other inseparable morphisms on $W_n$-valued local cohomology groups of RDPs. Then we consider RDP K3 surfaces admitting nontaut RDPs. We show that the height of the K3 surface, which is also defined in terms of the Frobenius action on $W_n$-valued cohomology groups, is related to the isomorphism class of the RDP.