On the harmonic volume of Fermat curves

On the harmonic volume of Fermat curves

We prove that B. Harris’ harmonic volume of the Fermat curve of degree nn is of infinite order if nn 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 bas...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2021-05, Vol.149 (5), p.1919-1928, Article 1919
Hauptverfasser: Eskandari, Payman, Murty, V. Kumar
Format: Artikel
Sprache:eng
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Research article
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Zusammenfassung:We prove that B. Harris’ harmonic volume of the Fermat curve of degree nn is of infinite order if nn 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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/15332