%0 Journal Article %A Broomhead, Nathan %A Ottem, John C. %A Prendergast, Artie %D 2015 %T Partially ample line bundles on toric varieties %U https://repository.lboro.ac.uk/articles/journal_contribution/Partially_ample_line_bundles_on_toric_varieties/9385364 %2 https://repository.lboro.ac.uk/ndownloader/files/16998560 %K untagged %K Mathematical Sciences not elsewhere classified %X Ample line bundles are a fundamental concept in algebraic geometry, encapsulating the central notion of positivity. A natural extension of the notion of ampleness is that of q- ampleness, for nonnegative integers q. Roughly speaking, q-ample line bundles on a variety are those which \kill cohomology in degrees above q." Line bundles of this kind have been studied by a number of authors, including Andreotti{Grauert [AG], Sommese [Som], Demailly{Peternell{Schneider [DPS], and Totaro [Tot]. %I Loughborough University