Topology and Factorization of Polynomials

2007/04/25 by Hani Shaker, Shaker, Hani
Mathematics · #12D05 (Primary) 14F40 #14J70(Secondary) #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #math.AG #math.AT #msc:12D05 #msc:14F40

paper · pdf · doi:10.48550/arxiv.0704.3363

Accepted in Mathematica Scandinavica. 8 pages

openalex publication_date 2007/04/25 · arxiv created 2008/04/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any polynomial P ∈ ℂ[X₁,X₂,...,X_n], we describe a ℂ-vector space F(P) of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of F(P) is the number of irreducible factors of P. Moreover, the knowledge of F(P) gives a complete factorization of the polynomial P by taking gcd's. This generalizes previous results by Ruppert and Gao in the case n=2.

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