Displaying similar documents to “On microlocal b -function”

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.

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 ∧ d Ω X , 0 n + 1 over ℂ { { ∂ t - 1 } } such that the action of t is expressed by t v = A 0 + A 1 ∂ 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.