Bivariate Factorization Using a Critical Fiber

We generalize the classical lifting and recombination scheme for rational and absolute factorization of bivariate polynomials to the case of a critical fiber. we explore different strategies for recombinations of the analytic factors, depending on the complexity of the ramification. we show that working along a critical fiber leads in some cases to a good theoretical complexity, due to the smaller number of analytic factors to recombine. we pay a particular attention to the case of polynomials that are non-degenerate with respect to their p-adic newton polytopes.