2015 Fiscal Year Final Research Report
Classification theory of projective varieties by Galois points and new developments
| Project/Area Number |
25800002
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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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) |
2013-04-01 – 2016-03-31
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| Keywords | ガロア点 / ガロワ点 / 正標数 / 射影代数多様体 / 射影 / ガロア群 / ガウス写像 / 準ガロア点 |
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| Outline of Final Research Achievements |
(1) I presented an upper bound for the number of inner Galois points for any plane curve in terms of the generic order of contact, the geometric genus and the degree, if the number is finite. (2) I presented a family of plane curves with two outer Galois points, and described the number of Galois points. (3) I characterized rational curves of degree four with two Galois points in characteristic zero. (4) I proposed the problem "When do Galois points coincide with rational points?" and I gave a characterization if the geometric genus is at most one. (5) I described the automrphism groups of smooth plane curves with two Galois points. (6) We studied the Galois closure for the dual curve and the point corresponding to an extendable Galois point (joint work with K. Miura). (7) We introduced the notion of the "quasi-Galois point" (joint work with T. Takahashi and K. Miura).
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| Free Research Field |
代数幾何
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