Griffiths group

In mathematics, more specifically in algebraic geometry, the Griffiths group of a projective complex manifold X measures the difference between homological equivalence and algebraic equivalence, which are two important equivalence relations of algebraic cycles.

More precisely, it is defined as

where Z k ( X ) denotes the group of algebraic cycles of some fixed codimension k and the subscripts indicate the groups that are homologically trivial, respectively algebraically equivalent to zero.

This group was introduced by Phillip Griffiths who showed that for a general quintic in P 4 (projective 4-space), the group Griff 2 ⁡ ( X ) is not a torsion group.