Families of polynomials and their specializations

2015/10/21 by Bodin, Arnaud, Dèbes, Pierre, Najib, Salah
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.06145

Abstract

For a polynomial in several variables depending on some parameters, we discuss some results to the effect that for almost all values of the parameters the polynomial is irreducible. In particular we recast in this perspective some results of Grothendieck and of Gao.

Related

• On some classes of irreducible polynomials
• Specializations of one-parameter families of polynomials
• Irreducibility of hypersurfaces
• Irreducibility of a sum of polynomials depending on disjoint sets of variables
• Explicit Hilbert Irreducibility