Ample subvarieties and q-ample divisors

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.

arXiv comment16 pages. 1 figure. Some new results added

References in corpus (2)

• A converse to the Andreotti-Grauert theorem
• Asymptotic cohomology vanishing and a converse to the Andreotti-Grauert theorem on surfaces

Cited by in corpus (1)

• Big $q$-ample Line Bundles