Summary: Deformations of Toric Singularities
Institut f¨ur reine Mathematik, HumboldtUniversit¨at zu Berlin
Ziegelstr. 13A, D10099 Berlin, Germany.
In the present paper we investigate the deformation theory of toric singularities (i.e. of those sin
gularities occurring in toric varieties). The best results are obtained for isolated toric Gorenstein
singularities: We describe their miniversal (or semiuniversal) deformation in several ways (by
a combinatorial construction, by equations, and by interpreting its irreducible components). See
section (1.2) for a more detailed survey.
My investigations on this subject started during a oneyear stay at the university of Kaiserslautern
(1990/91). I would like to thank Duco van Straten, GertMartin Greuel, and Theo de Jong for
turning my interest toward deformation theory and for many fruitful discussions and hints (and
the DFG for financial support).
At the same time I was introduced by Kurt Behnke, Jan Christophersen, and Jan Stevens to the
latest developments of deforming twodimensional quotient singularities. This led to the definition
of socalled toric deformations and my first attempts of classifying them. Then, during a short
stay (in 1992) at Cornell University, discussions with Bernd Sturmfels helped very much to form