Cycle classes on abelian varieties and the geometry of the Abel-Jacobi map
Algebraic Geometry
2023-07-07 v4
Abstract
We discuss two properties of an abelian variety, namely, being a direct summand in a product of Jacobians and the weaker property of being "split". We relate the first property to the integral Hodge conjecture for curve classes on abelian varieties. We also relate both properties to the existence problem for universal zero-cycles on Brauer-Severi varieties over abelian varieties. A similar relation is established for the existence problem of a universal codimension 2 cycle on a cubic threefold.
Keywords
Cite
@article{arxiv.2212.03046,
title = {Cycle classes on abelian varieties and the geometry of the Abel-Jacobi map},
author = {Claire Voisin},
journal= {arXiv preprint arXiv:2212.03046},
year = {2023}
}
Comments
Minor revision