Jef Laga

Vanishing criteria for Ceresa cycles

The Ceresa cycle is a canonical algebraic 1-cycle in the Jacobian of a curve with a marked point. In some sense it is the simplest non-trivial canonical algebraic cycle 'beyond homology' and as such it is a natural testing ground for our knowledge of cycles on abelian varieties. The Ceresa cycle vanishes for all hyperelliptic curves, but beyond this little is known about the locus of curves in Mg where this cycle is torsion. In this talk I will discuss joint work with Ari Shnidman where we study Ceresa cycles of curves with extra automorphisms and determine exactly which Picard curves have torsion Ceresa cycle.