A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic
Abstract
We prove some value of the harmonic volume for the Klein quartic $C$ is nonzero modulo ${1/2}\{mathbb Z}$, using special values of the generalized hypergeometric function ${}_3F_2$. This result tells us the algebraic cycle $C-C^-$ is not algebraically equivalent to zero in the Jacobian variety $J(C)$.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- August 2005
- DOI:
- arXiv:
- arXiv:math/0508433
- Bibcode:
- 2005math......8433T
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Geometric Topology;
- 14H30;
- 14H40;
- 30F30;
- 32G15
- E-Print:
- 8 pages, 1 figure