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Uniform stable radius and Milnor number for non-degenerate isolated complete intersection singularities
manuscripta mathematica ( IF 0.6 ) Pub Date : 2021-06-30 , DOI: 10.1007/s00229-021-01323-5
Tat Thang Nguyen

We prove that for two germs of analytic mappings \(f,g:({\mathbb {C}}^n,0) \rightarrow ({\mathbb {C}}^p,0)\) with the same Newton polyhedra which are (Khovanskii) non-degenerate and their zero sets are complete intersections with isolated singularity at the origin, there is a piecewise analytic family \(\{f_t\}\) of analytic maps with \(f_0=f, f_1=g\) which has a so-called uniform stable radius for the Milnor fibration. As a corollary, we show that their Milnor numbers are equal. Also, a formula for the Milnor number is given in terms of the Newton polyhedra of the component functions. This is a generalization of the result by C. Bivia-Ausina. Consequently, we obtain that the Milnor number of a non-degenerate isolated complete intersection singularity is an invariant of Newton boundaries.



中文翻译:

非退化孤立完全相交奇点的均匀稳定半径和米尔诺数

我们证明对于两个解析映射的胚芽\(f,g:({\mathbb {C}}^n,0) \rightarrow ({\mathbb {C}}^p,0)\)具有相同的牛顿多面体它们是 (Khovanskii) 非退化的并且它们的零集是在原点具有孤立奇点的完整交集,存在一个分段解析族\(\{f_t\}\)具有\(f_0=f, f_1=g \)其具有所谓的 Milnor 纤维化均匀稳定半径. 作为推论,我们证明他们的米尔诺数相等。此外,根据分量函数的牛顿多面体给出了米尔诺数的公式。这是 C. Bivia-Ausina 对结果的概括。因此,我们得到非退化孤立完全相交奇点的米尔诺数是牛顿边界的不变量。

更新日期:2021-07-01
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