Hypersurface sections of toric singularities (Q1192241)

The author studies Newton polyhedra for hypersurface sections of toric singularities. The author is mainly concerned with the case of periodicially elliptic singularities, i.e. singularities whose plurigenera do not exceed 1 and at least one plurigenus is equal to 1. In this connection the author gives a sufficient condition on the Newton polyhedron of the defining equation ensuring that a singularity be periodically elliptic. Under certain (rather restrictive) conditions the author gives an explicit construction of a (locally) semi-universal family of deformations of such singularities. It turns out that under these conditions a small deformation of a singularity of this type also has the same type. -- Many examples are studied in some detail.