Ample subvarieties and q-ample divisors

Details Ample subvarieties and q-ample divisors Ample subvarieties and q-ample divisors

2011-05-12

arxiv.org/abs/1105.2500v2

Mathematics

Algebraic Geometry

16 pages. 1 figure. Some new results added

Scientific paper

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.

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