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

TLDR: In this paper, the authors showed that the Milnor number of a non-degenerate isolated complete intersection singularity is invariant to the Newton polyhedra of the component functions.

Abstract: 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.