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

Abstract

52 pages, 2 figures, LaTeX + smf classes available at http://smf.emath.fr/Publications/Formats/index.html typos corrected, remarks added at the end of the introduction, in sect. 3, and a new appendix added. to appear in Ann. Institut Fourier (Grenoble)International audienceWe associate to any convenient nondegenerate Laurent polynomial 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 the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of the Laurent polynomial (or its universal unfolding) and of the corresponding Hodge theory