# Line bundles with partially vanishing cohomology

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 3, page 731-754
- ISSN: 1435-9855

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topTotaro, 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 -

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