Integral closure and bounds for quotients of multiplicities of monomial ideals

[EN] Given a pair of monomial ideals $I$ and $J$ of finite colength of the ring of analytic function germs $(\C^n,0)\to \C$, we prove that some power of $I$ admits a reduction formed by homogeneous polynomials with respect to the Newton filtration induced by $J$ if and only if the quotient of multip...

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Bibliographic Details
Author: Bivià-Ausina, Carles|||0000-0003-0784-3353
Format: article
Publication Date:2018
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/103293
Online Access:https://riunet.upv.es/handle/10251/103293
Access Level:Open access
Keyword:Integral closure of ideals
Mixed multiplicities of ideals
Monomial ideals
Newton polyhedra
MATEMATICA APLICADA
Description
Summary:[EN] Given a pair of monomial ideals $I$ and $J$ of finite colength of the ring of analytic function germs $(\C^n,0)\to \C$, we prove that some power of $I$ admits a reduction formed by homogeneous polynomials with respect to the Newton filtration induced by $J$ if and only if the quotient of multiplicities $e(I)/e(J)$ attains a suitable upper bound expressed in terms of the Newton polyhedra of $I$ and $J$. We also explore other connections between mixed multiplicities, Newton filtrations and the integral closure of ideals.