Partial positivity: geometry and cohomology of q-ample line bundles

Daniel, Greb and Küronya, Alex (2015) Partial positivity: geometry and cohomology of q-ample line bundles. LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES, 417. pp. 207-239. ISSN 0076-0552

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Abstract

We give an overview of partial positivity conditions for line bundles, mostly from a cohomological point of view. Although the current work is to a large extent of expository nature, we present some minor improvements over the existing literature and a new result: a Kodaira-type vanishing theorem for effective q-ample Du Bois divisors and log canonical pairs.

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