We introduce a notion of ampleness for subschemes of any 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. © 2012 Elsevier Inc..
Ottem, J. C. (2012). Ample subvarieties and q-ample divisors. Advances in Mathematics, 229(5), 2868–2887. https://doi.org/10.1016/j.aim.2012.02.001