LIMITS OF TANGENT SPACES OF A NORMAL SURFACE

We study the set of limiting tangent hyperplanes of normal surface ger m. We characterize these hyperplanes by the non-minimality of the Miln or number of their section with the surface. Then we generalize the re sults of [4] by means of weak simultaneous resolution of hyperplane se ctions family, and hence we precisely determine some exceptional tange nts of a normal surface singularity. Applying this, we prove that ''Ty urina components'' of a reasonable desingularization contract to fixed points of the linear system of polar curves. (C) Academie des Science s/Elsevier, Paris