| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
In this research, we studied the minimal value m(n) which satisfies the following property: the dimension of global section of m(K+L) is positive for any n-dimensional quasi-polarized manifolds (X,L) and every integer m which is greater than or equal to m(n), where K denotes the canonical divisor of X. Then we proved that m(n) is less than or equal to 2n-4. Moreover for the case of 4-dimensional polarized manifolds, we proved a conjecture which was proposed by Beltrametti and Sommese. Furthermore I studied the sectional genus and the sectional class, which are invariants of polarized manifolds, and I got several results which have been unknown.
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