Some results on Green's higher Abel-Jacobi map
Algebraic Geometry
2009-09-25 v1
Abstract
We study the higher Abel-Jacobi invariant defined recently by M. Green. We first construct a counterexample to the injectivity of Green's higher Abel-Jacobi map. On the other hand, we prove that the higher Abel-Jacobi map governs Mumford's pull-back of holomorphic forms. We deduce from this that if a surface has holomorphic 2-forms, the image of the higher Abel-Jacobi map, defined on its group of zero-cycles Albanese equivalent to 0, has infinite dimensional image.
Keywords
Cite
@article{arxiv.math/9903204,
title = {Some results on Green's higher Abel-Jacobi map},
author = {Claire Voisin},
journal= {arXiv preprint arXiv:math/9903204},
year = {2009}
}
Comments
23 pages, published version