Cycle exceptionnel de l'éclatement d'un idéal définissant l'origine de \({\mathbb C}^ n\) et applications. (Exceptional cycle of the blowing-up of an ideal defining the origin of \({\mathbb C}^ n\) and applications)
Let I be an ideal of \({\mathbb{C}}\{z_ 1,...,z_ n\}\) which defines the origin in \({\mathbb{C}}^ n\). Given a suitable choice of generators of \(I=(f_ 1,...,f_{n+p})\), we give an explicit method to determine the cycle of \({\mathbb{P}}^{n+p-1}\) associated with the exceptional fiber of the blowing-up of I in \({\mathbb{C}}^ n\). We also study the blowing-up of an equimultiple family of punctual ideals parametrized by a germ of a reduced complex analytic space.
blowing-up of an equimultiple family of punctual ideals
scientific article; zbMATH DE number 3995854
scientific article