English

Ample subvarieties and q-ample divisors

Algebraic Geometry 2011-10-10 v2

Abstract

We introduce a notion of ampleness for subschemes of higher codimension using the theory of q-ample line bundles. We also investigate certain geometric properties satisfied by ample subvarieties, e.g. the Lefschetz hyperplane theorems and numerical positivity. Using these properties, we also construct a counterexample to the converse of the Andreotti-Grauert vanishing theorem.

Keywords

Cite

@article{arxiv.1105.2500,
  title  = {Ample subvarieties and q-ample divisors},
  author = {John Christian Ottem},
  journal= {arXiv preprint arXiv:1105.2500},
  year   = {2011}
}

Comments

16 pages. 1 figure. Some new results added

R2 v1 2026-06-21T18:06:25.546Z