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

2005/08/23 by Tadokoro, Yuuki · 1 citation
#14H30 #14H40 #30F30 #32G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.math/0508433

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 ₃F₂. 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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