The log canonical threshold of products of ideals and mixed Łojasiewicz exponents

2024/09/21 by Carles Bivià-Ausina, Bivià-Ausina, Carles
Mathematics · #32S05 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2409.14251

openalex publication_date 2024/09/21 · openalex created_date 2024/10/26 · openalex updated_date 2026/08/01

Abstract

Given two ideals I and J of the ring \mathcal O_n of analytic function germs f:(\mathbb Cⁿ,0)→ \mathbb C, we show a sharp lower bound for the log canonical threshold of IJ in terms of the sequences of mixed Łojasiewicz exponents of them. In particular, in the case where J is the maximal ideal, the corresponding equality holds if and only if the integral closure of I equals some power of the maximal ideal.

Related

• Mixed Łojasiewicz exponents, log canonical thresholds of ideals and bi-Lipschitz equivalence
• The sequence of mixed Łojasiewicz exponents associated to pairs of ideals
• Multiplicities and log canonical threshold
• Log canonical threshold and diagonal ideals
• A sharp lower bound for the log canonical threshold