A study on the dimension of global sections of multiple adjoint bundle of polarized manifolds
| Project/Area Number |
24540043
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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 | Kochi University |
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Principal Investigator |
Fukuma Yoshiaki 高知大学, 自然科学系理学部門, 教授 (20301319)
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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 |
¥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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| Keywords | 代数学 / 偏極多様体 / 準偏極多様体 / 豊富な因子 / nefかつbigな因子 / 随伴束 / 断面不変量 |
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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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Report
(5 results)
Research Products
(13 results)
