2007/01/31 by Arnaud Bodin, Bodin, Arnaud, Pierre Dèbes +3
Computer Science · Mathematics · #11C08 #12E05 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.AC #math.AG #math.NT #msc:11C08 #msc:12E05
paper · pdf · doi:10.48550/arxiv.math/0701919
21 pages
arxiv created 2007/01/31 · openalex publication_date 2007/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a polynomial P in several variables over an algebraically closed field, we show that except in some special cases that we fully describe, if one coefficient is allowed to vary, then the polynomial is irreducible for all but at most deg(P)2-1 values of the coefficient. We more generally handle the situation where several specified coefficients vary.