Multivariate Bernstein-type Polynomials of Finitely Generated D-Modules
Commutative Algebra
2024-04-03 v1 Rings and Algebras
Abstract
We generalize the Gr\"obner basis method for free D-modules to the case of several term orderings induced by a partition of the set of basic variables. Using this generalized Gr\"obner basis technique we prove the existence and give a method of computation of a dimension polynomial in several variables associated with a finitely generated D-module. We show that this dimension polynomial carries more invariants of a D-module than the classical (univariate) Bernstein polynomial. We also show that the introduced multivariate dimension polynomial can be used for characterization of holonomic D-modules.
Cite
@article{arxiv.2404.02069,
title = {Multivariate Bernstein-type Polynomials of Finitely Generated D-Modules},
author = {Alexander Levin},
journal= {arXiv preprint arXiv:2404.02069},
year = {2024}
}