The applications of derived categories and topological methods to combinatorial commutative algebra
| Project/Area Number |
22540057
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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 Kohji 関西大学, システム理工学部, 准教授 (40283006)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 組合せ論的可換代数 / Borel fixed ideal / 極小自由分解 / 双対化複体 / アファイン半群環 / affine semigroup ring / toric face ring / 離散モース理論 / 単項式イデアル / (単項式イデアルの)polarization / Stanley depth / 局所双対性 |
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| Research Abstract |
Developing a result of Nagel and Reiner, the author and R. Okazaki studied the non-standard polarization of a Borel fixed ideal, and gave its minimal free resolution. This resolution is supported by a regular CW complex, which can be “interpreted” by the discrete Morse theory in the framework constructed by Welker et al.
The author also studied the dualizing complexes of seminormal affine semigroup rings and toric face rings. In this work, the preceding results of Bruns et al and Nguyes are re-formulated and improved using derived categories.
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Report
(4 results)
Research Products
(25 results)
