Milnor and Tjurina numbers for a hypersurface germ with isolated singularity

2017/08/31 by Yongqiang Liu, Liu, Yongqiang · 4 citations
Computer Science · Mathematics · #32S05 #32S25 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1708.09716

openalex publication_date 2017/08/31 · openalex created_date 2017/09/15 · openalex updated_date 2026/07/28

Abstract

Assume that f:(ℂⁿ,0) → (ℂ,0) is an analytic function germ at the origin with only isolated singularity. Let μ and τ be the corresponding Milnor and Tjurina numbers. We show that \dfracμτ ≤ n. As an application, we give a lower bound for the Tjurina number in terms of n and the multiplicity of f at the origin.

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