Jumps of Milnor numbers of Brieskorn-Pham singularities in\n non-degenerate families

2018/03/13 by Tadeusz Krasiński, Krasiński, Tadeusz, Justyna Walewska +1
Mathematics · #14B07 #32S30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1803.05324

openalex publication_date 2018/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The jump of the Milnor number of an isolated singularity f₀ is the\nminimal non-zero difference between the Milnor numbers of f₀ and one of\nits deformation (f_s). In the case f_s are non-degenerate singularities\nwe call the jump non-degenerate. We give a formula (an inductive algorithm\nusing diophantine equations) for the non-degenerate jump of f₀ in the case\nf₀ is a convenient singularity with only one (n-1)-dimensional face of\nits Newton diagram which equivalently (in our problem) can be replaced by the\nBrieskorn-Pham singularities.\n

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