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Invent. math. 128, 443479 (1997) c Springer-Verlag 1997
 

Summary: Invent. math. 128, 443­479 (1997)
c Springer-Verlag 1997
The versal deformation
of an isolated toric Gorenstein singularity
Klaus Altmann
Institut f¨ur Reine Mathematik, Humboldt-Universit¨at zu Berlin, Ziegelstr. 13A, D-10099 Berlin,
Germany (e-mail: altmann@mathematik.hu-berlin.de)
Oblatum 9-V-1996 & 30-IX-1996
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 so-called 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,

  

Source: Altmann, Klaus - Fachbereich Mathematik und Informatik & Institut für Mathematik, Freie Universität Berlin

 

Collections: Mathematics