Filtered restriction of geometric D-modules

Details Filtered restriction of geometric D-modules Filtered restriction of geometric D-modules

2012-01-20

arxiv.org/abs/1201.4259v1

Mathematics

Algebraic Geometry

Scientific paper

In D-module theory, we have the notion of the restriction of a module along a smooth variety. T. Oaku and N. Takayama have described a process to compute the restriction, which starts from a free resolution adapted to the V-filtration of Kashiwara-Malgrange. By using the theory of free resolutions adapted to the (order and V)-bifiltration (from T. Oaku , N. Takayama and M. Granger), we endow the restriction with an order filtration and we show that the process of Oaku and Takayama respects the order filtration. In consequence, we compute a minimal presentation of the algebraic local cohomology module associated with a quasi-homogeneous polynomial with an isolated singularity, viewed as a D-module and endowed with a kind of a pole order filtration.

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