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

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

2009-09-10

arxiv.org/abs/0909.1923v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

In this paper we construct a non-trivial element in the higher Griff{}iths
group $Griff ^{3,2}$ for the generic abelian fourfold $A^4$ with polarization
of type $(1,2,2,2)$. The key idea is to use that $A^4$ can be realized as a
generalized Prym variety and for this reason contains in a natural way some
curves i.e. dimension 1 cycles.

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