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Clusters of infinitely near points. (English) Zbl 0853.14002

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.

MSC:

14B10 Infinitesimal methods in algebraic geometry
14A05 Relevant commutative algebra
14L30 Group actions on varieties or schemes (quotients)
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