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MULTIPLICITY AND ŁOJASIEWICZ EXPONENT OF GENERIC LINEAR SECTIONS OF MONOMIAL IDEALS

Part of: Ring extensions and related topics Local rings and semilocal rings

Published online by Cambridge University Press:  20 February 2015

CARLES BIVIÀ-AUSINA
CARLES BIVIÀ-AUSINA*
Affiliation:
Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022 València, Spain email [email protected]
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Abstract

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We obtain a characterisation of the monomial ideals $I\subseteq \mathbb{C}[x_{1},\dots ,x_{n}]$ of finite colength that satisfy the condition $e(I)={\mathcal{L}}_{0}^{(1)}(I)\cdots {\mathcal{L}}_{0}^{(n)}(I)$, where ${\mathcal{L}}_{0}^{(1)}(I),\dots ,{\mathcal{L}}_{0}^{(n)}(I)$ is the sequence of mixed Łojasiewicz exponents of $I$ and $e(I)$ is the Samuel multiplicity of $I$. These are the monomial ideals whose integral closure admits a reduction generated by homogeneous polynomials.

Keywords

Łojasiewicz exponentsintegral closure of idealsmixed multiplicities of idealsmonomial idealsNewton polyhedra

MSC classification

Primary: 13B22: Integral closure of rings and ideals ; integrally closed rings, related rings (Japanese, etc.)
Secondary: 13H15: Multiplicity theory and related topics
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 2 , April 2015 , pp. 191 - 201
Copyright
Copyright © 2015 Australian Mathematical Publishing Association Inc. 

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