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arXiv · 1912.10655

Uniform stable radius and Milnor number for non-degenerate isolated complete intersection singularities

Tat Thang Nguyen
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Abstract

We prove that for two germs of analytic mappings $f,g\colon (\mathbb{C}^n,0) \rightarrow (\mathbb{C}^p,0)$ 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 {\it 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 invariance of Newton boundaries.

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Tat Thang Nguyen. 2019-12-23. Uniform stable radius and Milnor number for non-degenerate isolated complete intersection singularities. https://arxiv.org/abs/1912.10655

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