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

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

2002-11-22

arxiv.org/abs/math/0211352v2

Proceedings of the International Conference in Honor of Fr\'ed\'eric Pham (Nice, 2002). Ann. Inst. Fourier (Grenoble) 53 (2003

Mathematics

Algebraic Geometry

52 pages, 2 figures, LaTeX + smf classes available at http://smf.emath.fr/Publications/Formats/index.html typos corrected, rem

Scientific paper

We 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.

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