An algebraic approach to Nagata conjecture
Project/Area Number |
24540054
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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 | Meiji University |
Principal Investigator |
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Project Period (FY) |
2012-04-01 – 2016-03-31
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Project Status |
Completed (Fiscal Year 2015)
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Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
Keywords | 永田予想 / Cox環 / symbolic power / 有限生成 / Cox 環 / 標準因子 / 代数学 / 可換環論 / ヒルベルトの第14問題 / コーエンマコーレー錐 / Hilbert-Kunz 関数 / 因子類群 / 標準加群 |
Outline of Final Research Achievements |
Many reseachers studied the divisor class group and the canonical module of a Z~n-graded normal domain as Cox rings of normal projective varieties. We study the divisor class group and the canonical module for an N~n-graded normal domain. In order to describe them, we need some informations of divisors of the boundaries of N~n. We obtain latices if we divide the Grothendieck group and the Chow group by numerical equivalence. We tensor the real number field R with them, and consider the R-vector spaces. Consider the CM cone (the cone spanned by MCM's). We define the fundamental class of a ring in the vector space. We discuss whether it is in CM cone or not.
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Report
(5 results)
Research Products
(19 results)
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[Presentation] MCM加群で張られる錐2012
Author(s)
藏野和彦
Organizer
第 34 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 (葉山)
Year and Date
20121122-20121126
Related Report
Invited
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