Geodesic
Line bundles with partially vanishing cohomology
Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 731-754

Voir la notice de l'article provenant de la source EMS Press

Define a line bundle L on a projective variety to be q-ample, for a natural number q, if tensoring with high powers of L kills coherent sheaf cohomology above dimension q. Thus 0-ampleness is the usual notion of ampleness. We show that q-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 q-ampleness is a Zariski open condition, which is not clear from the definition.
DOI : 10.4171/jems/374
Classification : 14-XX, 32-XX, 00-XX
Keywords: Vanishing theorems, ample line bundles, q-ample line bundles, Castelnuovo–Mumford regularity, Koszul algebras, q-convexity 
@article{JEMS_2013_15_3_a1,
     author = {Burt Totaro},
     title = {Line bundles with partially vanishing cohomology},
     journal = {Journal of the European Mathematical Society},
     pages = {731--754},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2013},
     doi = {10.4171/jems/374},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/374/}
}
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Burt Totaro. Line bundles with partially vanishing cohomology. Journal of the European Mathematical Society, Tome 15 (2013) no. 3, pp. 731-754. doi: 10.4171/jems/374

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