Vanishing results in Chow groups for the modified diagonal cycles

We prove a sufficient condition for the vanishing of the modified diagonal cycle in the Chow group (with Q-coefficients) of the triple product of a curve over C. We exhibit infinitely many nonhyperelliptic curves, including the Fricke-Macbeath curve, the Bring curve, and two 1-dimensional families parameterized by certain Hurwitz spaces, for which our condition is satisfied.Contents 1. Introduction 1 2. Proof of the vanishing theorem 4 3. Hurwitz curves 8 4.More examples 13 References 15 1 deg c2(X) c 2 (X) ∈ Ch 2 (X) (note that deg c 2 (X) = 24) is the class of an F -point, and the class of ∆ e similarly defined by (1.1) vanishes in Ch 4 (X 3 ).