Abstract:We define an indicial polynomial of a $D$-module along an arbitrary subvariety as a generalization of both the classical indicial polynomial for a single linear differential equation and the Bernstein-Sato polynomial of a variety defined by Budur-Mustata-Saito. An indicial polynomial is also a generalization of the $b$-function of a $D$-module along a submanifold and can be used in the computation of the $D$-module theoretic inverse image by the embedding instead of the $b$-function. We consider properties of indicial polynomials and relations with $b$-functions. An indicial polynomial may exist even if the $b$-function does not, and gives the set of the roots of the $b$-function if it exists. Computation of an indicial polynomial is easier than the $b$-function and naturally includes the case with parameters.
From: Toshinori Oaku [view email]
[v1]
Wed, 27 May 2026 00:36:27 UTC (31 KB)
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