Clusters of infinitely near points (Q1923269)

The authors further develop the Zariski-Lipman theory of finitely supported complete (f.s.c.) ideals from the geometric point of view of clusters of infinitely near points. The main results are: a combinatorial characterization of the proximity relation as a generalized Enriques diagram; an explicit description of the monoid of f.s.c. monomial ideals as a polyhedral cone; a construction of such ideals by means of Newton polytopes; and the existence of a natural embedded resolution of a general complete intersection singularity associated to an f.s.c. ideal.