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Campillo, Antonio; Gonzalez-Sprinberg, Gérard; Lejeune-Jalabert, Monique

Clusters of infinitely near points. (English) Zbl 0853.14002

Math. Ann. 306, No. 1, 169-194 (1996).
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.
Reviewer: A.Campillo (Valladolid)

Cited in 1 Review
Cited in 21 Documents

MSC:

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

Keywords:

finitely supported complete ideals; Zariski-Lipman theory; infinitely near points; proximity relation; Enriques diagram; Newton polytopes
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\textit{A. Campillo} et al., Math. Ann. 306, No. 1, 169--194 (1996; Zbl 0853.14002)
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