English

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

Keywords

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}
}
R2 v1 2026-06-22T16:57:58.173Z