Albanese kernels and Griffiths groups

Abstract

We describe the Griffiths group of the product of a curve $C$ and a surface $S$ as a quotient of the Albanese kernel of $S$ over the function field of $C$. When $C$ is a hyperplane section of $S$ varying in a Lefschetz pencil, we prove the nonvanishing in $\text{Griff}(C\times S)$ of a modification of the graph of the embedding $C\hookrightarrow S$ for infinitely many members of the pencil, provided the ground field $k$ is of characteristic $0$, the geometric genus of $S$ is $>0$, and $k$ is large or $S$ is "of motivated abelian type".

To appear in the Tunisian J. Math

References in corpus (4)

• Unirational threefolds with no universal codimension 2 cycle
• On descending cohomology geometrically
• Torsion order of smooth projective surfaces
• The Brauer group and indecomposable (2,1)-cycles

Cited by in corpus (2)

• Chow-Lefschetz motives
• Refined height pairing