Some results on the higher Abel jacobi map for open varieties
Algebraic Geometry
2016-12-12 v5
Abstract
In this article, we study the infinitemisal invariant of the relative higher Abel Jacobi map of a smooth open morphism. We give a generalization of a theorem of Voisin to open varieties and higher Chow groups and as a corollary a non vanishing criterion for the higher Abel Jacobi map of a general open smooth hypersurface section of high degree of a smooth projective variety Y. On the other side, using Nori connectness theorem, the image of the primitive part of the higher Abel Jacobi map of a general open smooth hypersurface section of high degree of a smooth projective variety Y is generated by the image of the restriction of a primitive cycle on the corresponding affine subset of Y
Cite
@article{arxiv.1611.06375,
title = {Some results on the higher Abel jacobi map for open varieties},
author = {Johann Bouali},
journal= {arXiv preprint arXiv:1611.06375},
year = {2016}
}