| Project/Area Number |
22740001
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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 | Yamagata University |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
|
| Project Status |
Completed (Fiscal Year 2012)
|
| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 代数幾何 / ガロア点 / 正標数 / 射影代数多様体 / 射影 / ガロア群 / ガウス写像 / 射影代数名様体 |
|---|
| Research Abstract |
(1) I completely settled the distribution of Galois points for a smooth plane curve in positive characteristic. (2) Generalizing the Klein quartic in characteristic two, I gave a family of curves with at least two Galois points. (3) I showed that Galois points for a certain rational plane curve coincide with rational points over a finite field. (4) As a joint work with Homma and Kim, we showed that the curves in (3) induce good algebraic-geometric codes. (5) As a joint work with Miura, we studied the relationship between Galois points and dual curves (in characteristic zero), and showed that the dual curve of a smooth plane curve does not have a Galois point.
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