Vanishing criteria for Ceresa cycles

Abstract: The Ceresa cycle of a curve is perhaps the simplest example of a homologically trivial algebraic cycle which need not be algebraically trivial. Its vanishing in the Chow (resp. Griffiths) group has various implications, but the locus of vanishing Ceresa cycles in $M_g$ is quite mysterious, beyond the fact that it contains the hyperelliptic locus. I'll present new vanishing criteria for the Ceresa cycle of curves with automorphisms, one of them conditional on the Hodge conjecture. In certain low genus cases the relevant Hodge conjecture is known, and using this we describe the locus of Picard curves with vanishing Ceresa cycle. This is joint work with Jef Laga.

number theory

Audience: researchers in the topic

BC-MIT number theory seminar