A formula for jumping numbers in a two-dimensional regular local ring

In this article we give an explicit formula for the jumping numbers of an ideal of finite colenght in a two-dimensional regular local ring with an algebraically closed residue field. For this purpose, we associate a certain numerical semigroup to each vertex of the dual graph of a log-resolution of the ideal.Comment: 32 pages, to appear in Journal of Algebr

On the exceptional locus of the birational projections of normal surface singularity into a plane

Given a normal surface singularity $(X, Q)$ and a birational morphism to a non- singular surface $\pi : X \to S$, we investigate the local geometry of the exceptional divisor $L$ of $\pi$. We prove that the dimension of the tangent space to $L$ at $Q$ equals the number of exceptional components meeting at $Q$. Consequences relative to the existence of such birational projections contracting a prescribed number of irreducible curves are deduced. A new characterization of minimal singularities is obtained in these terms.Comment: 12 pages, 2 figure

Configurations of infinitely near points

We present a survey of some aspects and new results on configurations, i.e. disjoint unions of constellations of infinitely near points, local and global theory, with some applications and results on generalized Enriques diagrams, singular foliations, and linear systems defined by clusters