On the harmonic volume of Fermat curves

Eskandari, Payman; Murty, V.

doi:10.1090/proc/15332

On the harmonic volume of Fermat curves
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by Payman Eskandari and V. Kumar Murty PDF

Proc. Amer. Math. Soc. 149 (2021), 1919-1928 Request permission

Abstract:

We prove that B. Harris’ harmonic volume of the Fermat curve of degree $n$ is of infinite order if $n$ has a prime divisor greater than 7. The statement is equivalent to the statement that the Griffiths’ Abel-Jacobi image of the Ceresa cycle of such a curve is of infinite order for every choice of base point. In particular, these cycles are of infinite order modulo rational equivalence.

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