2015 Fiscal Year Final Research Report
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 |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Meiji University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 永田予想 / Cox環 / symbolic power / 有限生成 |
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| 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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| Free Research Field |
代数学
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