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

摘要

In this paper we construct a non-torsion element in the higher Griffiths group Griff 3,2(A 4) for the generic abelian fourfold A 4 with polarization of type (1,2,2,2). The key idea is to use the fact that A 4 can be realized as a generalized Prym variety which naturally contains some curves, i.e. dimension 1 cycles.