Diplomarbeit
Nathan Ilten
"On toric deformations of cyclic quotient singularities"
Von 1.12.2006 bis 30.3.2007
Betreuer: Prof. Dr. Klaus Altmann
In comparison to other singularities, the deformation theory of cyclic quotient is less complicated; there is even a canonical description of the versal deformation. This diploma thesis analyzes the deformation theory of these objects from a combinatorial perspective, using the correspondence of cyclic quotient singularities to two dimensional affine toric varieties. Combinatorial criterion are provided for determining to which versal base components one-parameter toric deformations maps. A particularily exact description is made in the case of T-singularities. Finally, a method for constructing certain non-homogeneous multi-parameter toric deformations is described.
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