Local symmetries of finite type hypersurfaces in C~2

摘要

The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C~2. It is also proved that, with the exception of hypersurfaces of the form v = |z|~k, local automorphisms are always determined by their 1-jets. Using this result, the second part describes special normal forms which by an additional normalization eliminate the nonlinear symmetries of the model and allows to decide effectively about local equivalence of two hypersurfaces given in this normal form.