Application of New Methods of Combinatorial Topology to Commutative Algebra

• 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
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• 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 / アファイン有向マトロイド / 正則CW複体 / 局所コホモロジー / cd指数

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.

Research Products

• [Journal Article] A Canonical module characterization of Serre's (R_1) (2017)
  • Author(s): Lukas katthaen, Kohji Yanagawa
  • Journal Title: Communications in Algebra Volume: 未定
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Properties of Lyubeznik numbers under localization and polarization (2015)
  • Author(s): Arindam Banerjee, Luis Nunez-Betancourt, Kohji Yanagawa
  • Journal Title: Journal of Pure and Applied Algebra Volume: 219 Issue: 11 Pages: 4872-4888
  • DOI: 10.1016/j.jpaa.2015.03.010
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Dualizing complexes of seminormal affine semigroup rings and toric face rings (2015)
  • Author(s): Kohji Yanagawa
  • Journal Title: Journal of Algebra Volume: 425 Pages: 367-391
  • DOI: 10.1016/j.jalgebra.2014.11.013
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Squarefree P-modules and the cd-index (2014)
  • Author(s): Satoshi Murai, Kohji Yanagawa
  • Journal Title: Advances in Mathematics Volume: 265 Pages: 241-279
  • DOI: 10.1016/j.aim.2014.07.037
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Addendum to “Frobenius and Cartier algebras of Stanley-Reisner rings” [J. Algebra 358 (2012) 414-425] (2014)
  • Author(s): Josep Alvarez-Montaner, Kohji Yanagawa
  • Journal Title: Journal of Algebra Volume: 未定 Pages: 300-304
  • DOI: 10.1016/j.jalgebra.2013.09.006
  • Peer Reviewed
• [Journal Article] On CW complexes supporting Eliahou-Kervaire type resolutions of Borel fixed ideals (2014)
  • Author(s): Ryota Okazaki, Kohji Yanagawa
  • Journal Title: Collectanea Mathematica Volume: 未定 Issue: 1 Pages: 125-147
  • DOI: 10.1007/s13348-014-0104-0
  • Peer Reviewed
• [Presentation] Lyubeznik numbers of local rings and linear strands of graded ideals (2016)
  • Author(s): Kohji Yanagawa
  • Organizer: International Conference and 8th Japan-Vietnam joint Seminar on Commutative Algebra
  • Place of Presentation: Ha Long, Vietnam
  • Year and Date: 2016-03-21
• [Presentation] The Cohen{Macaulayness of the bounded complex of an affine oriented matroid (2015)
  • Author(s): Ryota Okazaki, Kohji Yanagawa
  • Organizer: 第37回可換環論シンポジウム
  • Place of Presentation: 倉敷シーサイドホテル（岡山）
  • Year and Date: 2015-11-18
• [Presentation] アフィン有向マトロイドのbounded complex のCohen-Macaulay 性とマトロイド・イデアルのCohen-Macaulay性 (2015)
  • Author(s): 岡崎亮太, 柳川浩二
  • Organizer: 日本数学会 2015年度秋季総合分科会
  • Place of Presentation: 京都産業大学
  • Year and Date: 2015-09-13
• [Presentation] Lyubeznik numbers of local rings and linear strands of graded ideals (2014)
  • Author(s): Kohji Yanagawa
  • Organizer: 第36回可換環論シンポジウム
  • Place of Presentation: IPC 生産性国際交流センター （神奈川）
  • Year and Date: 2014-11-24
• [Presentation] 有向マトロイドに付随する単項式イデアル (2014)
  • Author(s): 柳川浩二
  • Organizer: 組合せ論と可換代数サマーセミナー２０１４
  • Place of Presentation: 宮島コーラルホテル (広島)
  • Year and Date: 2014-09-23
• [Presentation] 単項式イデアルの Lyubeznik table
  • Author(s): 柳川浩二
  • Organizer: 組合せ論と可換代数サマーセミナー
  • Place of Presentation: 下関市生涯学習プラザ（山口）
• [Presentation] 多面体的複体の flag f-列について
  • Author(s): 村井聡, 柳川浩二
  • Organizer: 日本数学会2014年度年会
  • Place of Presentation: 学習院大学(東京)