Zero-dimensional Gorenstein algebra with the strong Lefschets properties
Project/Area Number |
24540050
|
Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Tokai University |
Principal Investigator |
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Project Period (FY) |
2012-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
|
Keywords | Lefschetz Properties / 0次元ゴレンスタイン環 / 完全交叉環 / Sperner 性 / ヒルベルト関数 / 次数付き環 / コホモロジー環 / 巾ゼロ元 / アルティン可換環 / 強いレフシェッツ条件 / 弱いレフシェッツ条件 / Sperner 理論 / 平坦拡大定理 / 部分環定理 / Tolgiatti Theorem / アルティン環 / 有限半順序集合 / 不変式部分環 / ゴレンスタイン環 / レフシェッツ条件 / シュペルナ性 / 高次ヘシアン / Hard Lefschetz Theorem |
Outline of Final Research Achievements |
In September, 2013, I published a book entitled "The Lefschetz Properties," with 5 Japanese coauthors. It took 10 years to write this book. In the course of writing the book, it turned out that the topic has many ties to other areas of algebra. In September 2012, I organized a workshop in Hawaii Tokai International College, where 13 researchers from Japan, USA, Sweden and Germany, gathered and we reported the latest results and exchanged ideas. In March, 2015, I organized a workshop in Goettingen, Germany, for the second time, under a cooperation with German and American and Spanish researchers, where more or less 25 researchers came together and we exchanged ideas and new results. It is scheduled to have such a workshop at Banff, Canada in 2016 for the third time.
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Report
(4 results)
Research Products
(17 results)
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[Book] The Lefschetz Properties2013
Author(s)
Harima, Tadahito; Maeno, Toshiaki; Morita, Hideaki; Numata, Yasuhide; Wachi, Akihito; Watanabe, Junzo.
Total Pages
250
Publisher
Springer
Related Report
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