1-Semiquasihomogeneous Singularities of Hypersurfaces - Pathology in Characteristic 2

: In the preceding paper [7], the classification of 1-semiquasihomogeneous singularities of hypersurfaces in arbitrary characteristic p was given. They turn out to be defined (up to quadratic suspensions) by the equations given by K. Saito [9] over the base field of complex numbers, as far as p<F NaN> 6= 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 ~ E 6 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). 0. The problem k denotes an algebraically closed field. Consider indeterminates X := (X 0 ; : : : ; X n ) equipped with positive weights w i := w(X i ) 2 I Q and a formal power series f 2 k[[X]] consisting of monomials m of weight w(m ) := w() := P i w i 1 such that the "pr..