2015 Fiscal Year Final Research Report
Construction of concrete theory of Abelian functions focusing the multivariate sigma functions
| Project/Area Number |
25400010
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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 | Meijo University (2014-2015)
University of Yamanashi (2013) |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | Abelian function / Jacobian variety / Abelian variety / algebraic curve |
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| Outline of Final Research Achievements |
(1) I published a paper on new addition formulae for genus one case, which is a result of collaboration with J.C. Eilbeck and M. England. (2) I generalized the result in (1) to any plane telescopic curves. I am writing a paper on this. (3) I discovered that the sigma functions have Hurwitz integrality on the power series expansion at the origin. (4) I proved this phenomenon, wrote a paper, and submitted it.
\item I had talks in Japan on the results of (2) and (3). (5) According to my best knowledge, there is no explicit description of example of Abelian variety which has non-Galois complex multiplication. I found it and wrote a note on it. You can download it from my web page. (6) I invited Eilbeck in order to research on the theory of heat equations satisfied by the sigma functions. We two got a large amount of results by this research. We are writing papers on the results.
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| Free Research Field |
Abel 函数論
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