We give formulas for the image Milnor number of a weighted-homogeneous map-germ \(({\mathbb {C}}^n,0)\rightarrow ({\mathbb {C}}^{n+1},0)\), for \(n=4\) and 5, in terms of weights and degrees. Our expressions are obtained by a purely interpolative method, applied to a result by Ohmoto. We use our approach to recover the formulas for \(n=2\) and 3 due to Mond and Ohmoto, respectively. For \(n\ge 6\), the method is valid as long as certain multi-singularity conjecture holds.

中文翻译：

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加权均质图谱的图像米尔诺数公式

我们给出加权齐次映射胚芽的图像米尔诺数公式\(({\mathbb {C}}^n,0)\rightarrow ({\mathbb {C}}^{n+1},0) \)，对于\(n=4\)和 5，在权重和度数方面。我们的表达式是通过纯粹的插值方法获得的，应用于 Ohmoto 的结果。我们使用我们的方法来恢复\(n=2\)和 3 的公式，分别归因于 Mond 和 Ohmoto。对于\(n\ge 6\)，只要某些多奇点猜想成立，该方法就有效。