Displaying similar documents to “Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)”

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 { { 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.