Bruce-Roberts Numbers and Quasihomogeneous Functions on Analytic Varieties

2022/12/04 by Carles Bivià-Ausina, Bivià-Ausina, Carles, Konstantinos Kourliouros +3
Mathematics · #32S05 #32S50 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2212.01919

openalex publication_date 2022/12/04 · openalex created_date 2022/12/18 · openalex updated_date 2026/07/28

Abstract

Given a germ of an analytic variety X and a germ of a holomorphic function f with a stratified isolated singularity with respect to the logarithmic stratification of X, we show that under certain conditions on the singularity type of the pair (f,X), the following relative analog of the well known K. Saito's theorem holds true: equality of the relative Milnor and Tjurina numbers of f with respect to X (also known as Bruce-Roberts numbers) is equivalent to the relative quasihomogeneity of the pair (f,X), i.e. to the existence of a coordinate system such that both f and X are quasihomogeneous with respect to the same positive rational weights.

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