Mixed Łojasiewicz exponents and \(\log\) canonical thresholds of ideals
type: Item
instance of: scholarly article
title: Mixed Łojasiewicz exponents and \(\log\) canonical thresholds of ideals
zbMATH Open document ID: 1336.32027
author: Carles Bivià-Ausina
author: T. Fukui
published in: Journal of Pure and Applied Algebra
publication date: 2015-10-27T00:00:00Z
review text: Let \({\mathcal O}_n\) be the ring of holomorphic germs \(f:({\mathbb{C}}^n,0)\to \mathbb{C}\). Given a monomial ideal \(I\) of finite colength in \({\mathcal O}_n\), one of the goals of the article is to provide a description, in terms of the Newton polyhedron of \(I\), of the family of Łojasiewicz exponents of \(I\) introduced in [the first author, Math. Z. 262, No. 2, 389--409 (2009; Zbl 1168.32022)]. Some inequalities relating Łojasiewicz exponents and mixed multiplicities are also obtained. Given an ideal \(I\) of finite colength, the authors also study the relation between the sequence of log canonical thresholds of the restrictions of \(I\) to linear subspaces of different dimensions with Łojasiewicz exponents and they obtain an expression for this sequence in terms of Newton polyhedra when the ideal \(I\) is monomial.
reviewed by: Vincent Thilliez
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 13H15
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 6499132
zbMATH Keywords: complex singularities
zbMATH Keywords: ideals
zbMATH Keywords: multiplicities
zbMATH Keywords: Łojasiewicz exponents
zbMATH Keywords: log-canonical threshold
describes a project that uses: SINGULAR
MaRDI profile type: Publication
full work available at URL: j.jpaa.2015.06.007
OpenAlex ID: W2237573438
cites work: Resolution of Singularities and Division of Distributions
cites work: Semianalytic and subanalytic sets
cites work: Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
cites work: Local Łojasiewicz exponents, Milnor numbers and mixed multiplicities of ideals
cites work: Joint reductions of monomial ideals and multiplicity of complex analytic maps
cites work: JACOBIAN IDEALS AND THE NEWTON NON-DEGENERACY CONDITION
cites work: Łojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations
cites work: Łojasiewicz exponents and resolution of singularities
cites work: Newton filtrations, graded algebras and codimension of non-degenerate ideals
cites work: Q5465147
cites work: Sur les exposants de Lojasiewicz
cites work: Q4097535
cites work: The Łojasiewicz exponent of semiquasihomogeneous singularities
cites work: Multiplicities and log canonical threshold
cites work: A characterization of semi-quasihomogeneous functions in terms of the Milnor number
cites work: Constant Milnor number implies constant multiplicity for quasihomogeneous singularities
cites work: Resolution of singularities. A research textbook in tribute to Oscar Zariski. Based on the courses given at the working week in Obergurgl, Austria, September 7--14, 1997
cites work: Q4040095
cites work: Asymptotic Samuel function of hyperplane sections and multiplicity
cites work: The Bhattacharya Function of Complete Monomial Ideals in Two Variables
cites work: Multiplier ideals of monomial ideals
cites work: Q3414477
cites work: The \(j\)-multiplicity of monomial ideals
cites work: Polyedres de Newton et nombres de Milnor
cites work: The Łojasiewicz exponent of an isolated weighted homogeneous surface singularity
cites work: Q4650504
cites work: Integral closure of ideals and equisingularity
cites work: Une estimation asymptotique du nombre de solutions approchées d'une équation p-adique. (Asymptotic estimation of the number of approximate solutions of a p-adic equation)
cites work: Q3719034
cites work: Multiplier ideals and integral closure of monomial ideals: An analytic approach
cites work: Singular Points of Complex Hypersurfaces. (AM-61)
cites work: On the Milnor number of a generic hyperplane section
cites work: Singularities of pairs via jet schemes
cites work: IMPANGA lecture notes on log canonical thresholds Notes by Tomasz Szemberg
cites work: Topologically Trivial Deformations of Isolated Quasihomogeneous Hypersurface Singularities are Equimultiple
cites work: Semicontinuity of the {\L}ojasiewicz exponent
cites work: Q3810114
cites work: Q3701763
cites work: Q3995023
cites work: Generalizations of Reductions and Mixed Multiplicities
cites work: General elements and joint reductions
cites work: Mixed Multiplicities, Joint Reductions and Quasi-Unmixed Local Rings
cites work: Some Resonances of Łojasiewicz Inequalities
cites work: Variétés polaires. I: Invariants polaires des singularites d'hypersurfaces
cites work: Q4047653
cites work: Positivity of mixed multiplicities
cites work: Q4750108
DOI: 10.1016/J.JPAA.2015.06.007
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