On the Abel–Jacobi maps of Fermat Jacobians
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- 作者：Noriyuki Otsubo (1)
- 关键词：Algebraic cycle ; Iterated integral ; Hypergeometric function ; 14C25 ; 33C20 ; 33C65
- 刊名：Mathematische Zeitschrift
- 出版年：2012
- 出版时间：2 - February 2012
- 年：2012
- 卷：270
- 期：1
- 页码：423-444
- 全文大小：315KB
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1. Department of Mathematics and Informatics, Chiba University, Yayoicho 1-33, Inage, Chiba, 263-8522, Japan - ISSN：1432-1823
文摘
We study the Abel–Jacobi image of the Ceresa cycle ${W_k-W_k^-}$ , where W k is the image of the kth symmetric product of a curve X on its Jacobian variety. For the Fermat curve of degree N, we express it in terms of special values of generalized hypergeometric functions and give a criterion for the non-vanishing of ${W_k-W_k^-}$ modulo algebraic equivalence, which is verified numerically for some N and k.