Application of Koszul duality to commutative algebra
| Project/Area Number |
19540028
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kansai University |
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Principal Investigator |
YANAGAWA Kouji Kansai University, システム理工学部, 准教授 (40283006)
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| Co-Investigator(Kenkyū-buntansha) |
和久井 道久 関西大学, システム理工学部, 専任講師 (60252574)
毛利 出 静岡大学, 理学部, 准教授 (50436903)
寺井 直樹 佐賀大学, 文化教育学部, 准教授 (90259862)
若松 隆義 埼玉大学, 教育学部, 教授 (00192435)
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| Co-Investigator(Renkei-kenkyūsha) |
TERAI Naoki 佐賀大学, 文化教育学部, 准教授 (90259862)
WAKUI Michihisa 関西大学, システム理工学部, 講師 (60252574)
MORI Izuru 静岡大学, 理学部, 准教授 (50436903)
WAKAMATSU Takayoshi 埼玉大学, 教育学部, 教授 (00192435)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 組合せ論的可換代数 / Stanley-Reisner環 / アファイン半群環 / 導来圏 / Koszul双対性 / 双対化複体 / 単体的半順序集合 / 局所双対性 / ポアンカレ・ヴェルディエ双対性 / toric face ring / Castelnuovo-Mumford regularity / linearity defect / dualizing complex / 石田複体 |
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| Research Abstract |
The author has been applied the theory of derived categories (e.g., Koszul duality) to the study of combinatorial commutative algebra. The main aim of this research project was to extend this idea and results to general commutative algebra. In this direction, results related to the coherent property of rings were obtained, and the paper was published in an academic journal in 2009. Around 2008, the author slightly changed the direction of the research, and begun to study relatively new objects of combinatorial commutative algebra for which we cannot use usual methods. In this direction, the author has written several papers. Some of them have been published in an academic journal.
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Report
(4 results)
Research Products
(23 results)
