We describe a new construction to obtain a simple hypersurface singularity from the corresponding simple complex Lie-group
G. Let
X be the closed orbit in the projective space attached to the Lie algebra
\mathfrakg\mathfrak{g}
of
G. Consider a regular nilpotent element
y0 Î \mathfrakgy_0 \in \mathfrak{g}
and denote by
H
y
0 the hyperplane orthogonal to
y
0 with respect to the Killing form. Then the hyperplane section
X
H
y
0, has exactly one singularity which is simple of desired type. By variation of the point
y
0 we obtain a versal deformation. The construction generalizes with minor modifications to any characteristic
p of the basefield. Even in bad characteristic we recover at least the positive part of the semiuniversal deformation. We prove that for
p=2 a simple, quasihomogeneous singularity of type A
7 resp. D
8 is adjacent to E
7 resp. E
8 provided its dimension is even. Furthermore A
8 is adjacent to E
8 for
p=3.
Unterstützt durch den Schweizerischen Nationalfonds