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- W2962783509 abstract "Given a $D$-module $M$ generated by a single element, and a polynomial $f$, one can construct several $D$-modules attached to $M$ and $f$ and can define the notion of the (generalized) $b$-function following M. Kashiwara. These modules are closely related to the localization and the local cohomology of $M$. We show that the $b$-function, if it exists, controls these modules and present general algorithms for computing these modules and the $b$-function if it exists without any further assumptions. We also give some examples of multiplicity computation of such $D$-modules including a possibly well-known explicit formula for the localization of the polynomial ring by a hyperplane arrangement." @default.
- W2962783509 created "2019-07-30" @default.
- W2962783509 creator A5011323533 @default.
- W2962783509 date "2019-03-07" @default.
- W2962783509 modified "2023-09-23" @default.
- W2962783509 title "Localization, local cohomology, and the $b$-function of a $D$-module with respect to a polynomial" @default.
- W2962783509 doi "https://doi.org/10.2969/aspm/07710353" @default.
- W2962783509 hasPublicationYear "2019" @default.
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