Application of New Methods of Combinatorial Topology to Commutative Algebra

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400057
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kansai University
• Principal Investigator: Yanagawa Kohji 関西大学, システム理工学部, 教授 (40283006)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 組合せ論的可換代数 / 単項式イデアル / Lyubeznik 数 / 極小自由分解 / CW胞体 / 有向マトロイド

Outline of Final Research Achievements

With Spanish and American coauthors, I studied the Lyubeznik numbers of the quotient rings of polynomial rings by monomial ideals. For example, we showed that the procedure of "polarization" essentially preserves this invariant. With Prof. S. Murai, I studied the "cd-index" of flag complexes using the notion of squarefree modules. I also studied cellular free resolutions of monomial ideals with Prof. R. Okazaki. We applied this method to the study of affine oriented matroids.

Free Research Field

数物系科学