CURVES AND PROXIMITY ON RATIONAL SURFACE SINGULARITIES

We study the germs of curves in a rational surface singularity (S,P) f rom the point of view of proximity, classifying them up to a notion of equisingularity. We introduce the concept of cluster of infinitely ne ar points and we use it to generalize the Hoskin-Deligne formula, and to give an algorithm to describe a minimal system of generators of a c omplete ideal in the local ring O-S,O-P. (C) 1997 Elsevier Science B.V .