Clusters of infinitely near points Antonio Campillo1, Gerard Gonzalez-Sprinberg2, Monique Lejeune-Jalabert2 1 Departamento de Algebra y Geometrıa, Universidad de Valladolid, E-47005 Valladolid (Spain), email: . 2 Institut Fourier, Universite de Grenoble I, UMR 5582U, BP74, 38402 Saint Martin d'Heres (France), email: , Summary. In this article we further develop 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 polhyedral 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 a f.s.c. ideal. Introduction In [E.C] (L. IV, chap. II, 17), Enriques and Chisini consider systems of plane curves which pass with assigned multiplicities through an assigned set of infinitely near points of a (proper) point of the plane.
- point blowing-ups
- reducible curves
- qi ≥
- irreducible curves contracted
- zariski's theory
- linear equivalence
- ideals endowed
- ideals
- any point