 
Summary: Invent. math. 128, 443479 (1997)
c SpringerVerlag 1997
The versal deformation
of an isolated toric Gorenstein singularity
Klaus Altmann
Institut f¨ur Reine Mathematik, HumboldtUniversit¨at zu Berlin, Ziegelstr. 13A, D10099 Berlin,
Germany (email: altmann@mathematik.huberlin.de)
Oblatum 9V1996 & 30IX1996
Abstract. Given a lattice polytope Q Rn
, we define an affine scheme ¯M
that reflects the possibilities of splitting Q into a Minkowski sum. Denoting by
Y the toric Gorenstein singularity induced by Q, we construct a flat family over
¯M with Y as special fiber. In case Y has an isolated singularity, this family is
versal.
1 Introduction
(1.1) The whole deformation theory of an isolated singularity is encoded in
its socalled versal deformation. For complete intersection singularities this is a
family over a smooth base space obtained by certain perturbations of the defining
equations.
As soon as we leave this class of singularities, the structure of the family,
