2011 Fiscal Year Final Research Report
The harmonic volume for compact Riemann surfaces as a function on the moduli space of Riemann surfaces.
| Project/Area Number |
21740057
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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 |
Geometry
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| Research Institution | Kisarazu National College of Technology |
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Principal Investigator |
TADOKORO Yuuki 木更津工業高等専門学校, 基礎学系, 准教授 (10435414)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 調和体積 / 反復積分 / リーマン面 / モジュライ空間 / 写像類群 / トポロジー |
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| Research Abstract |
Harris defined the harmonic volume for compact Riemann surfaces, using Chen's iterated integrals. It depends only on the complex structure of compact Riemann surfaces. We obtain the trace map images of the values of certain harmonic volumes for some cyclic quotients of Fermat curves. These provide the algorithm showing that the algebraic cycles called by the Ceresa cycles are not algebraically equivalent to zero in the Jacobian varieties. We apply the method to the case for the prime N<1000 with N=1 modulo 3.
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