Holomorphic Equivalence and Nonlinear Symmetries of Ruled Hypersurfaces in C-2

摘要

We solve the local equivalence problem for ruled hypersurfaces in C-2 at a point of infinite type by giving a normal form. We describe all ruled hypersurfaces which admit nonlinear symmetries and give their complete characterization according to the dimension of their automorphism group. As an application, we give a bound for the dimension of the stability group for a family of nonminimal hypersurfaces.