On the numerical dimension of pseudo-effective divisors in positive characteristic
Algebraic Geometry
2013-06-13 v3
Abstract
Let X be a smooth projective variety over an algebraically closed field of positive characteristic. We prove that if D is a pseudo-effective R-divisor on X which is not numerically equivalent to the negative part in its divisorial Zariski decomposition, then the numerical dimension of D is positive. In characteristic zero, this was proved by Nakayama using vanishing theorems.
Keywords
Cite
@article{arxiv.1206.6521,
title = {On the numerical dimension of pseudo-effective divisors in positive characteristic},
author = {Paolo Cascini and Christopher Hacon and Mircea Mustata and Karl Schwede},
journal= {arXiv preprint arXiv:1206.6521},
year = {2013}
}
Comments
v.3 (17 pages): typos corrected and other minor changes. Additional remarks on the singular case. To appear in the American Journal of Mathematics