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arXiv · 1105.2500

Ample subvarieties and q-ample divisors

John Christian Ottem
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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.

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John Christian Ottem. 2011-05-12. Ample subvarieties and q-ample divisors. https://arxiv.org/abs/1105.2500

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