We study the equisingularity of a family of function germs \(\{f_t:(X_t,0)\rightarrow ({\mathbb {C}},0)\}\), where \((X_t,0)\) are d-dimensional isolated determinantal singularities. We define the \((d-1)\)th polar multiplicity of the fibers \(X_t\cap f_t^{-1}(0)\) and we show how the constancy of the polar multiplicities is related to the constancy of the Milnor number of \(f_t\) and the Whitney equisingularity of the family.

中文翻译：

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关于孤立行列式奇异性的函数族的等价性

我们研究了功能细菌家族\（\ {f_t：（X_t，0）\ rightarrow（{\ mathbb {C}}，0）\} \）的等价性，其中\（（X_t，0）\）是d维孤立的行列式奇点。我们定义了纤维的第（{d-1）\）个极数\（X_t \ cap f_t ^ {-1}（0）\），并展示了极性的多重性的恒定性与纤维的恒定性之间的关系。\（f_t \）的米尔诺数与家庭的惠特尼等价性。