Complete ideals and singularities of curves

Abstract

his is an expository paper in Spanish of results published by the author. No proofs are given in this paper. Let us recall that Zariski has proved the unique factorisation of complete ideals into simple complete ideals in a local regular ring of dimension two. In dimension larger than 3, the author recalls Lipman's Theorem of factorisation of finitely supported complete ideals into ∗-simple complete ideals. In this decomposition "negative powers'' can appear. The main result of this paper gives conditions on the sequence of infinitely near points in order to have only positive powers in this decomposition.