Abstract
Let and be non-constant, complex, polynomial function-germs at the origin such that . We suppose that and have an isolated singularity at and the same Milnor number (respectively, the same Teissier -sequence). We show that if and can be connected by a continuous path in the -constant (respectively, -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
Christophe Eyral. Mutsuo Oka. "On paths in the -constant and -constant strata." Hiroshima Math. J. 54 (2) 157 - 167, July 2024. https://doi.org/10.32917/h2023001
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