On Smoothable Curve Singularities: Local Methods.
We determine conditions in order that a differentiable function be approximable from above by analytic functions, being left invariate on a fixed analytic subset which is a locally complete intersection.
Let be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring ; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.
A dual space of the Tjurina algebra attached to a non-quasihomogeneous unimodal or bimodal singularity is considered. It is shown that almost every algebraic local cohomology class, belonging to the dual space, can be characterized as a solution of a holonomic system of first order differential equations.
In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold , with 1- dimensional exceptional set and finitely generated second homology group , is embeddable in if and only if is Kähler, and this case occurs only when does not contain any effective curve which is a boundary.