 
Summary: One parameter families containing three
dimensional toric Gorenstein singularities
Klaus Altmann
Contents
1 Introduction 1
2 Visualizing T 1 3
3 Genuine deformations 9
4 Three dimensional toric Gorenstein singularities 14
5 Work in progress and open problems 24
1 Introduction
1.1
Let be a rational, polyhedral cone and Y = Y the aÆne toric variety
it denes, which is normal but possibly singular; we study the deformation
theory of Y . The innitesimal deformation space T 1
Y is a multigraded vector
space, with homogeneous pieces determined by the combinatorial formulas of
[Al 1].
If Y has only an isolated Gorenstein singularity, we can say even more
(cf. [Al 2], [Al 3]): T 1 is concentrated in a single multidegree, and the cor
responding homogeneous piece has an elementary geometric description in
