Curves and proximity on rational surface singularities Original Research Article

We study the germs of curves in a rational surface singularity (S,P) from the point of view of proximity, classifying them up to a notion of equisingularity. We introduce the concept of cluster of infinitely near 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 complete ideal in the local ring images, p.