2011/05/12 by Ottem, John Christian · 1 citation
#14C20 #14C25 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1105.2500
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.