Grothendieck--Lefschetz for ample subvarieties
Algebraic Geometry
2023-02-07 v4
Abstract
We establish a Grothendieck--Lefschetz theorem for smooth ample subvarieties of smooth projective varieties over an algebraically closed field of characteristic zero and, more generally, for smooth subvarieties whose complement has small cohomological dimension. A weaker statement is also proved in a more general context and in all characteristics. Several applications are included.
Cite
@article{arxiv.1911.10385,
title = {Grothendieck--Lefschetz for ample subvarieties},
author = {Tommaso de Fernex and Chung Ching Lau},
journal= {arXiv preprint arXiv:1911.10385},
year = {2023}
}
Comments
v4: to appear in Math. Z. v5: 19 pages; an error in Theorem B about torsion in positive characteristics, kindly pointed out by Emelie Arvidsson and Lena Ji, is fixed; applications are unaffected