Open Access
July 2024 On paths in the μ-constant and μ*-constant strata
Christophe Eyral, Mutsuo Oka
Author Affiliations +
Hiroshima Math. J. 54(2): 157-167 (July 2024). DOI: 10.32917/h2023001

Abstract

Let f and f be non-constant, complex, polynomial function-germs at the origin 0n such that f(0)=f(0)=0. We suppose that f and f have an isolated singularity at 0 and the same Milnor number (respectively, the same Teissier μ*-sequence). We show that if f and f can be connected by a continuous path in the μ-constant (respectively, μ*-constant) stratum, then they can also be connected by a piecewise complex-analytic path (defined in the relevant natural way) in this stratum.

Acknowledgement

We are grateful to the referee for his/her valuable comments and suggestions, especially for suggesting Remark 5.3.

Citation

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Christophe Eyral. Mutsuo Oka. "On paths in the μ-constant and μ*-constant strata." Hiroshima Math. J. 54 (2) 157 - 167, July 2024. https://doi.org/10.32917/h2023001

Information

Received: 21 February 2023; Revised: 27 April 2023; Published: July 2024
First available in Project Euclid: 18 July 2024

Digital Object Identifier: 10.32917/h2023001

Subjects:
Primary: 14B05 , 32S05

Rights: Copyright © 2024 Hiroshima University, Mathematics Program

Vol.54 • No. 2 • July 2024
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