Analytic Improper Intersections I: Deformation to the Normal Cone

摘要

In this paper we present in the algebraic setting an intersection algorithm considered by Tworzewski [22], which is a local analytic counterpart of the Stuckrad-Vogel intersection algorithm from global algebraic geometry (cf.[20, 5]). Some other local algebraic counterparts have been investigated by Achilles and Manaresi [1, 2]. The main purpose is to provide in this analytic context the significant method of deformation to the normal cone, which is one of the most powerful tools of intersection theory (cf.[4, 5, 2, 10]). For some important refinements and applications of this method we refer the reader to our next article [11].