Greb, D.; Küronya, A. 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]. Cited in 7 Documents MSC: 14C20 Divisors, linear systems, invertible sheaves PDFBibTeX XMLCite \textit{D. Greb} and \textit{A. Küronya}, Lond. Math. Soc. Lect. Note Ser. 417, 207--239 (2014; Zbl 1326.14012) Full Text: arXiv