On stable polynomial mappings

2020/06/16 by Michał Farnik, Zbigniew Jelonek, Farnik, Michał +1
Mathematics · #14R99 #32A10 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2006.09039

openalex publication_date 2020/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For given natural numbers d₁,d₂ let Ω₂(d₁,d₂) be the set off all polynomial mappings F=(f,g):ℂ²→ℂ² such that deg f≤ d₁, deg g≤ d₂. We say that the mapping F is topologically stable in Ω₂(d₁,d₂) if for every small deformation F_t∈ Ω₂(d₁,d₂) the mapping F_t is topologically equivalent to the mapping F. The aim of this paper is to characterize the topologically stable mappings in Ω₂(d₁,d₂). In particular we show how to effectively determine a member of Ω₂(d₁,d₂) with generic topology.

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