Roczen, Marko
1-Semiquasihomogeneous Singularities of Hypersurfaces - Pathology in Characteristic 2
Preprint series:
Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)
- MSC:
- 14B05 Singularities, See also {14E15, 14H20, 32Sxx, 58C27}
- 14B12 Local deformation theory, Artin approximation, etc., See also {13B40, 13D10}
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).
AMS classification: 14B05, 14B12,
keywords: semiquasihomogeneous
singularities, base field of positive characteristic
Keywords: semiquasihomogeneous singularities, base field of positive characteristic