Line bundles with partially vanishing cohomology

Totaro, Burt. "Line bundles with partially vanishing cohomology." Journal of the European Mathematical Society 015.3 (2013): 731-754. <http://eudml.org/doc/277186>.

@article{Totaro2013,
abstract = {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.},
author = {Totaro, Burt},
journal = {Journal of the European Mathematical Society},
keywords = {vanishing theorems; ample line bundles; $q$-ample line bundles; Castelnuovo-Mumford regularity; Koszul algebras; $q$-convexity; ample line bundles; -ample line bundles; Castelnuovo-Mumford regularity; Koszul algebras; -convexity},
language = {eng},
number = {3},
pages = {731-754},
publisher = {European Mathematical Society Publishing House},
title = {Line bundles with partially vanishing cohomology},
url = {http://eudml.org/doc/277186},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Totaro, Burt
TI - Line bundles with partially vanishing cohomology
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 3
SP - 731
EP - 754
AB - 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.
LA - eng
KW - vanishing theorems; ample line bundles; $q$-ample line bundles; Castelnuovo-Mumford regularity; Koszul algebras; $q$-convexity; ample line bundles; -ample line bundles; Castelnuovo-Mumford regularity; Koszul algebras; -convexity
UR - http://eudml.org/doc/277186
ER -