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Deformations of Toric Singularities Klaus Altmann

Summary: Deformations of Toric Singularities
Klaus Altmann
Institut f¨ur reine Mathematik, Humboldt­Universit¨at zu Berlin
Ziegelstr. 13A, D­10099 Berlin, Germany.
E­mail: altmann@mathematik.hu­berlin.de

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


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


Collections: Mathematics