Linear differential operators for polynomial equations

Given a squarefree polynomial P ε k0 [x, y], k0 a number field, we construct a linear differential operator that allows one to calculate the genus of the complex curve defined by P = 0 (when P is absolutely irreducible), the absolute factorization of P over the algebraic closure of k0, and calculate information concerning the Galois group of P over k̄0 (x) as well as over k0(x). © 2002 Elsevier Science Ltd. All rights reserved.