Applications of algebraic local cohomology to hypersurface singularities

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17513
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: The University of Tokushima
• Principal Investigator: Nabeshima Katsusuke 徳島大学, 大学院社会産業理工学研究部(理工学域), 准教授 (00572629)
• Research Collaborator: TAJIMA Shinichi 筑波大学, 数理物質系(数学域), 教授
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 代数的局所コホモロジー / 孤立特異点 / アルゴリズム / 包括的グレブナー基底系 / Limiting tangnet space / 変形チュリナ数 / local Euler obstruction

Outline of Final Research Achievements

We have given algorithms and implementations for computing invariants of hypersurface isolated singularities (i.e., Limiting tangent space, μ*-sequence, integral number, local Euler obstruction, Tjurina stratifications of μ-constant deformations). Furthermore, we have introduced algorithms for solving ideal membership problems in local rings and computing comprehensive Groebner systems in PBW algebras. These algorithms are useful to study hypersurface singularities.

Free Research Field

計算機代数学