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 over such that the action of is expressed by
for two matrices with semi-simple, where is the basis. As an application, we calculate the -function of 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 sur telle que l’action de s’écrit
pour deux matrices avec semi-simple, où est la base. Comme application, on calcule la -fonction de 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}, pages = {27--72}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {39}, number = {1}, year = {1989}, doi = {10.5802/aif.1157}, mrnumber = {91i:32035}, zbl = {0644.32005}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1157/} }
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/articles/10.5802/aif.1157/
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