%0 Journal Article
%T Ample subvarieties and q-ample divisors
%A John Christian Ottem
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1105.2500v2