Factoring bivariate polynomials using adjoints

We relate factorization of bivariate polynomials to singularities of projective plane curves. We prove that adjoint polynomials of a polynomial F∈k[x,y] with coefficients in a field k permit to recombinations of the factors of F(0,y) induced by both the absolute and rational factorizations of F, and so without using Hensel lifting. We show in such a way that a fast computation of adjoint polynomials leads to a fast factorization. Our results establish the relations between the algorithms of Duval-Ragot based on locally constant functions and the algorithms of Lecerf and Chèze-Lecerf based on lifting and recombinations. The proof is based on cohomological sequences and residue theory.