Period mapping via Brieskorn modules

Morihiko Saito

Displaying similar documents to “Period mapping via Brieskorn modules”

On the structure of Brieskorn lattice

Morihiko Saito (1989)

Annales de l'institut Fourier

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We study the structure of the filtered Gauss-Manin system associated to a holomorphic function with an isolated singularity, and get a basis of the Brieskorn lattice $Ω_{X, 0}^{n + 1} / d f \land d Ω_{X, 0}^{n + 1}$ over $ℂ {{\partial_{t}^{- 1}}}$ such that the action of $t$ is expressed by $t v = A_{0} + A_{1} \partial_{t}^{- 1} v$ for two matrices $A_{0}, A_{1}$ with $A_{1}$ semi-simple, where $v =^{t} (v_{1} ... v_{μ})$ is the basis. As an application, we calculate the $b$ -function of $f$ in the case of two variables.

On microlocal $b$ -function

Morihiko Saito (1994)

Bulletin de la Société Mathématique de France

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

Antoine Douai, Claude Sabbah (2003)

Annales de l’institut Fourier

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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 the 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.