  One relates factorization of bivariate polynomials to singularities of
projective plane curves. One proves that adjoint polynomials permit to solve
the recombinations of the modular factors induced by the absolute and rational
factorizations, and so without using Hensel's lifting. One establishes in such
a way the relations between the algorithm of Duval-Ragot (locally constant
functions) and of Ch\`eze-Lecerf (lifting and recombinations), and one shows
that a fast computation of adjoint polynomials leads to a fast factorization.
The proof is based on cohomological sequences and residue theory.
