For each N 2, Asakura and Otsubo have recently introduced a smooth family of algebraic curves \X₍, ⏚\⏚ ℉ \₀, ₁, \ in characteristic 0 that is closely related to hypergeometric functions and the Fermat curve of degree N. In this paper, we study the Gross-Kudla-Schoen modified diagonal 1-cycles of these curves. We prove that if p 3 is a prime, then for every λ the Griffiths Abel-Jacobi image of the modified diagonal cycle of X, ⏚ is nontrivial for every cuspidal choice of a base point. On the other hand, we show that the modified diagonal cycle and hence the Ceresa cycle of X₃, ⏚ is torsion in the Chow group for every λ and every choice of a base point.
Eskandari et al. (Fri,) studied this question.