Computing Holonomic D-Modules Associated to a Family of Non-isolated Hypersurface Singularities via Comprehensive Grobner Systems of PBW Algebra

被引：0

作者：

Tajima, Shinichi ^{[1
]}

Nabeshima, Katsusuke ^{[2
]}

Ohara, Katsuyoshi ^{[3
]}

Umeta, Yoko ^{[4
]}

机构：

[1] Niigata Univ, Grad Sch Sci & Technol, 8050 Ikarashi 2 No Cho,Nishi Ku, Niigata, Japan

[2] Tokyo Univ Sci, Dept Appl Math, 1-3 Kagurazaka,Shinjuku Ku, Tokyo, Japan

[3] Kanazawa Univ, Fac Math & Phys, Kakuma, Kanazawa, Japan

[4] Josai Univ, Dept Math, 3-26 Kioicho,Chiyoda Ku, Tokyo, Japan

来源：

MATHEMATICS IN COMPUTER SCIENCE | 2023年 / 17卷 / 01期

关键词：

Comprehensive Grobner system; Poincare-Birkhof-Witt algebra; Non-isolated singularity; Holonomic D-module; Local cohomology; B-FUNCTIONS; ALGORITHMS; IDEALS; ROOTS;

D O I：

10.1007/s11786-022-00553-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The reduced b-functions and the relevant holonomic D-modules associated to a family of hypersurfaces with non-isolated singularities are considered in the context of symbolic computation. Based on the theory of comprehensive Grobner systems, algorithms of computing reduced b-functions and holonomic D-modules for parametric cases are introduced. A strategy for analyzing holonomic D-modules is described. Main ingredients of our approach are comprehensive Grobner systems on Poincare-Birkhoff-Witt algebra and local cohomology.

引用

页数：22

共 5 条

[1] Computing Holonomic D-Modules Associated to a Family of Non-isolated Hypersurface Singularities via Comprehensive Gröbner Systems of PBW Algebra
Shinichi Tajima
Katsusuke Nabeshima
Katsuyoshi Ohara
Yoko Umeta
Mathematics in Computer Science, 2023, 17
[2] Comprehensive Grobner systems in PBW algebras, Bernstein-Sato ideals and holonomic D-modules
Nabeshima, Katsusuke
Ohara, Katsuyoshi
Tajima, Shinichi
JOURNAL OF SYMBOLIC COMPUTATION, 2018, 89 : 146 - 170
[3] On holonomic D-modules attached to Reiffen's hypersurface isolated singularities
Tajima S.
Nakamura Y.
Journal of Mathematical Sciences, 2009, 158 (2) : 288 - 296
[4] Comprehensive Grobner Systems in Rings of Differential Operators, Holonomic D-modules and B-functions
Nabeshima, Katsusuke
Ohara, Katsuyoshi
Tajima, Shinichi
PROCEEDINGS OF THE 2016 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION (ISSAC 2016), 2016, : 349 - 356
[5] Brieskorn modules and gauss-manin systems for non-isolated hypersurface singularities
Barlet, Daniel
Saito, Morihiko
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2007, 76 : 211 - 224

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