JournalsjemsVol. 15, No. 3pp. 731–754

Line bundles with partially vanishing cohomology

  • Burt Totaro

    University of Cambridge, United Kingdom
Line bundles with partially vanishing cohomology cover
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Abstract

Define a line bundle LL on a projective variety to be qq-ample, for a natural number qq, if tensoring with high powers of LL kills coherent sheaf cohomology above dimension qq. Thus 0-ampleness is the usual notion of ampleness. We show that qq-ampleness of a line bundle on a projective variety in characteristic zero is equivalent to the vanishing of an explicit finite list of cohomology groups. It follows that qq-ampleness is a Zariski open condition, which is not clear from the definition.

Cite this article

Burt Totaro, Line bundles with partially vanishing cohomology. J. Eur. Math. Soc. 15 (2013), no. 3, pp. 731–754

DOI 10.4171/JEMS/374