Testing the non-vanishing of the Ceresa cycle of $X_0(N)$
For a curve $C$ and a fixed degree-one divisor $e$ of $C$, we can embed $C$ into its Jacobian. This embedding induces an algebraic $1$-cycle on the Jacobian called the Ceresa cycle, which we denote by $\mathrm{Cer}(C,e)$. Although homologically trivial, Ceresa cycles of very general curves with genus $\geq 3$ are non-trivial under algebraic equivalence. It is generally unknown whether a very general curve admits a non-trivial Ceresa cycle modulo rational equivalence. In this paper, we explore the non-triviality under rational equivalence of the Ceresa cycle corresponding to the modular curve…
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