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Partial positivity: geometry and cohomology of \(q\)-ample line bundles. (English) Zbl 1326.14012

Hacon, Christopher D. (ed.) et al., Recent advances in algebraic geometry. A volume in honor of Rob Lazarsfeld’s 60th birthday. Based on the conference, Ann Arbor, MI, USA, May 16–19, 2013. Cambridge: Cambridge University Press (ISBN 978-1-107-64755-8/pbk; 978-1-107-41600-0/ebook). London Mathematical Society Lecture Note Series 417, 207-239 (2014).
Summary: 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 expository in nature, we present some minor improvements on the existing literature and a new result: a Kodaira-type vanishing theorem for effective \(q\)-ample Du Bois divisors and log canonical pairs.
For the entire collection see [Zbl 1318.14002].

MSC:

14C20 Divisors, linear systems, invertible sheaves
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