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

2019/12/23 by Tat Thang Nguyen, Nguyen, Tat Thang
Mathematics · #14B05 #14B07 #14D05 #14D06 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1912.10655

openalex publication_date 2019/12/23 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We prove that for two germs of analytic mappings f,g colon (\ℂⁿ,0)\n\→ (\ℂ^p,0) with the same Newton polyhedra which are\n(Khovanskii) non-degenerate and their zero sets are complete intersections with\nisolated singularity at the origin, there is a piecewise analytic family\n f_t of analytic maps with f₀=f, f₁=g which has a so-called it\nuniform stable radius for the Milnor fibration. As a corollary, we show that\ntheir Milnor numbers are equal. Also, a formula for the Milnor number is given\nin terms of the Newton polyhedra of the component functions. This is a\ngeneralization of the result by C. Bivia-Ausina. Consequently, we obtain that\nthe Milnor number of a non-degenerate isolated complete intersection\nsingularity is an invariance of Newton boundaries.\n

Related

• On the Milnor fibration of certain Newton degenerate functions
• Durfee-type bound for some non-degenerate complete intersection\n singularities
• Lower bound of Newton number
• The degeneration of the boundary of the Milnor fibre to the link of\n complex and real non-isolated singularities
• Arnold's problem on monotonicity of the Newton number for surface\n singularities