Hilbert’s irreducibility theorem for linear differential operators

Abstract

We prove a differential analogue of Hilbert's irreducibility theorem. Let L be a linear differential operator with coefficients in C(X)(x) that is irreducible over C(X)¯(x), where X is an irreducible affine algebraic variety over an algebraically closed field C of characteristic zero. We show that the set of c∈X(C) such that the specialized operator Lc of L remains irreducible over C(x) is Zariski dense in X(C).

Locations

• arXiv (Cornell University) - View - PDF
• Communications in Algebra - View