Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)

We associate to any convenient nondegenerate Laurent polynomial f on the complex torus (ℂ*)ⁿ a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of Die Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of f (or its universal unfolding) and of the corresponding Hodge theory.