A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic

Details A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic

2005-08-23

arxiv.org/abs/math/0508433v1

Mathematics

Algebraic Geometry

8 pages, 1 figure

Scientific paper

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 $J(C)$.

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