On the Lefschetz property of complete intersections
| Project/Area Number |
15K04812
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Niigata University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
和地 輝仁 北海道教育大学, 教育学部, 准教授 (30337018)
五十川 読 熊本高等専門学校, 共通教育科(八代キャンパス), 教授 (80223056)
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| Research Collaborator |
Watanabe Junzo
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 可換環 / 完全交叉環 / アルティン環 / ゴレンスタイン環 / レフシェッツ性 / 対称式 / 終結式 / 可換環論 / 完全交叉 / Macaulay dual generator / m-fullness / componentwise m-fullness / Macaulayの双対元 / completely m-fullness / componentwise linearity / EGH予想 / Sperner性 / matching性 / filterwise m-fullness |
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| Outline of Final Research Achievements |
We studied the Lefschetz property of complete intersections. Main results of this research are the followings: 1. Any quadratic complete intersection with certain action of the symmetric group has the strong Lefschetz property. 2. Suppose that the EGH Conjecture is true for a complete intersection A. Then A has the Sperner property. 3. All complete intersections defined by products of general linear forms have the strong Lefschetz property. 4. We gave a characterization of the Macaulay dual generators for quadratic complete intersections. 5. We gave another proof of some known results on power sum symmetric polynomials in three variables.
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| Academic Significance and Societal Importance of the Research Achievements |
完全交叉のレフシェッツ性に関する研究は、コンピュータサイエンスとも関連のある多項式環論の基礎研究の一つである。また、レフシェッツ性は、線形写像の最強のジョルダン分解を求める問題とも関連しており、今後、線形写像のレフシェッツ性は、代数学の基本的な事項として位置付けられるのではないだろうか。
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Report
(5 results)
Research Products
(21 results)
