  We propose a new lifting and recombination scheme for rational bivariate
polynomial factorization that takes advantage of the Newton polytope geometry.
We obtain a deterministic algorithm that can be seen as a sparse version of an
algorithm of Lecerf, with now a polynomial complexity in the volume of the
Newton polytope. We adopt a geometrical point of view, the main tool being
derived from some algebraic osculation criterions in toric varieties.
