1-Semiquasihomogeneous Singularities of Hypersurfaces - Pathology in Characteristic 2

Abstract

In a preceding paper, the classification of 1-semiquasihomogeneous singularities of hypersurfaces in arbitrary characteristic p was given. They turn out to coincide (up to quadratic suspensions) with the equations given by K. Saito over the base field of complex numbers, as far as the characteristic p of the base field is different from 2. For p=2, the even- and odd dimensional case have to be distinguished, and there are nontrivial superdiagonal deformations in the odd- dimensional case. The singularity ~E6 gives an infinite family of nonisomorphic singularities with fixed principal part, contrary to the classical case of simple elliptic singularities, which have modality 1 (coming from the absolute invariant in the principal part).