Studies on cycles of intermediate dimensions on toric varieties
| Project/Area Number |
20740026
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Gifu Shotoku Gakuen University |
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Principal Investigator |
SATO Hiroshi Gifu Shotoku Gakuen University, 経済情報学部, 准教授 (20433310)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 代数学 / 幾何学 / トーリック多様体 / ファノ多様体 / 森理論 / トーリック様体 / 双有理幾何学 / 導来圏 / 2-サイクル |
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| Research Abstract |
In this research, we mainly studied two-cycles on smooth projective toric varieties. Our main purpose is to construct a similar theory to the toric Mori theory for two-cycles, and as a result, we obtained a method to describe two-cycles combinatorially by using the data of the corresponding fan. Moreover, we investigated cones of effective two-cycles on toric varieties, and obtained the classification of toric varieties whose second Chern character is non-negative for certain special cases. In connection with this research, we obtained some results about the ordinary toric Mori theory.
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Report
(5 results)
Research Products
(26 results)
