A moving lemma for cycles with very ample modulus
Algebraic Geometry
2016-10-05 v3
Abstract
We prove a moving lemma for higher Chow groups with modulus, in the sense of Binda-Kerz-Saito, of projective schemes when the modulus is given by a very ample divisor. This provides one of the first cases of moving lemmas for cycles with modulus, not covered by the additive higher Chow groups. We apply this to prove a contravariant functoriality of higher Chow groups with modulus. We use our moving techniques to show that the higher Chow groups of a line bundle over a scheme, with the 0-section as the modulus, vanishes.
Keywords
Cite
@article{arxiv.1507.05429,
title = {A moving lemma for cycles with very ample modulus},
author = {Amalendu Krishna and Jinhyun Park},
journal= {arXiv preprint arXiv:1507.05429},
year = {2016}
}
Comments
v1: 22 pages / v2: 25 pages. Revised and some materials added / v3: 24 pages. Section 7 of v2 removed because there was an error. Other parts were revised. A version of this article was accepted by Annali della SNS di Pisa