Infinitesimal Deformations of Cusp Singularities.
We prove that every injective endomorphism of an affine algebraic variety over an algebraically closed field of characteristic zero is an automorphism. We also construct an analytic curve in ℂ⁶ and its holomorphic bijection which is not a biholomorphism.
The pseudometric of Hahn is identical to the Kobayashi-Royden pseudometric on domains of dimension greater than two. Thus injective hyperbolicity coincides with ordinary hyperbolicity in this case.
We give a description of bounded pseudoconvex Reinhardt domains, which are complete for the Carathéodory inner distance.
A description of bounded pseudoconvex Reinhardt domains, which are complete with respect to the inner -th Carathéodory-Reiffen distance, is given.
We study the normalization of analytic vector fields with a nilpotent linear part. We prove that such an analytic vector field can be transformed into a certain form by convergent transformations when it has a non-singular formal integral. We then prove that there are smoothly linearizable parabolic analytic transformations which cannot be embedded into the flows of any analytic vector fields with a nilpotent linear part.
We give a necessary condition for a holomorphic vector field to induce an integrable osculating plane distribution and, using this condition, we give a characterization of such fields. We also give a generic classification for vector fields which have two invariant coordinate planes.