On the rationality of deformations of singularities of type A, D, E

Details On the rationality of deformations of singularities of type A, D, E On the rationality of deformations of singularities of type A, D, E

2012-01-04

arxiv.org/abs/1201.0936v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

We study deformations of the Klein surfaces obtained as quotient of finite linear groups of automorphisms of the plane; this surfaces are of type A, D, E, corresponding to their singularities. The deformation is proved to be not rational in cases D, E, although it is obviously rational in the case A. The group of automorphisms of the Klein surfaces is also described, and is linear and of finite dimension in cases D, E; this result being obviously false in case A.

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