| 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)
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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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