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

Antoine Douai; Claude Sabbah

doi:10.5802/aif.1974

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

Antoine Douai
, Claude Sabbah

Université Côte D’Azur

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1055-1116+xiv+xviii
Journal	Annales de l'Institut Fourier
Volume	53
Issue number	4
DOIs	https://doi.org/10.5802/aif.1974
Publication status	Published - 1 Jan 2003

Keywords

Brieskorn lattice
Gauss-Manin system
Probenius manifold

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abstract = "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.",

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AU - Sabbah, Claude

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N2 - 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.

AB - 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.

KW - Brieskorn lattice

KW - Gauss-Manin system

KW - Probenius manifold

UR - https://www.scopus.com/pages/publications/1642304869

U2 - 10.5802/aif.1974

DO - 10.5802/aif.1974

M3 - Article

AN - SCOPUS:1642304869

SN - 0373-0956

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SP - 1055-1116+xiv+xviii

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 4

ER -

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

Abstract

Keywords

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