Mixed Łojasiewicz exponents, log canonical thresholds of ideals and bi-Lipschitz equivalence

2014/05/08 by Carles Bivià-Ausina, Bivià-Ausina, Carles, Toshizumi Fukui +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1405.2110

openalex publication_date 2014/05/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the Łojasiewicz exponent and the log canonical threshold of ideals of \mathcal O_n when restricted to generic subspaces of \mathbb Cⁿ of different dimensions. We obtain effective formulas of the resulting numbers for ideals with monomial integral closure. An inequality relating these numbers is also proven. We also introduce the notion of bi-Lipschitz equivalence of ideals and we prove the bi-Lipschitz invariance of Łojasiewicz exponents and log canonical thresholds of ideals.

Citations

• IMPANGA lecture notes on log canonical thresholds

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