Algebraic cycles on the generic abelian fourfold with polarization of type (1,2,2,2)

Abstract

In this paper we construct a non-torsion element in the higher Griffiths group Griff 3,2(A4) for the generic abelian fourfold A4 with polarization of type (1,2,2,2). The key idea is to use the fact that A4 can be realized as a generalized Prym variety which naturally contains some curves, i.e. dimension 1 cycles.