On the structure of Brieskorn lattice
Annales de l'Institut Fourier, Volume 39 (1989) no. 1, p. 27-72

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 /dfdΩ X,0 n+1 over {{ t -1 }} such that the action of t is expressed by

tv=A0+A1t-1v

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 étudie la structure du système de Gauss-Manin filtré associé à une fonction holomorphe à singularité isolée, et on obtient une base du réseau de Brieskorn Ω X,0 n+1 /dfdΩ X,0 n+1 sur {{ t -1 }} telle que l’action de t s’écrit

tv=A0=A0+A1t-1v

pour deux matrices A 0 ,A 1 avec A 1 semi-simple, où v= t (v 1 ,...,v μ ) est la base. Comme application, on calcule la b-fonction de f dans le cas en deux variables.

@article{AIF_1989__39_1_27_0,
     author = {Saito, Morihiko},
     title = {On the structure of Brieskorn lattice},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {39},
     number = {1},
     year = {1989},
     pages = {27-72},
     doi = {10.5802/aif.1157},
     zbl = {0644.32005},
     mrnumber = {91i:32035},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1989__39_1_27_0}
}
Saito, Morihiko. On the structure of Brieskorn lattice. Annales de l'Institut Fourier, Volume 39 (1989) no. 1, pp. 27-72. doi : 10.5802/aif.1157. http://www.numdam.org/item/AIF_1989__39_1_27_0/

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