ON THE NUMERICAL DIMENSION OF PSEUDO-EFFECTIVE DIVISORS IN POSITIVE CHARACTERISTIC

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....

Full description

Saved in:
Bibliographic Details
Published in:American journal of mathematics 2014-12, Vol.136 (6), p.1609-1628
Main Authors: Cascini, Paolo, Hacon, Christopher, Mustaţă, Mircea, Schwede, Karl
Format: Article
Language:English
Subjects:
Algebra
Grants
Integers
Linear systems
Map algebra
Mathematical functions
Mathematical problems
Mathematical theorems
Morphisms
Research fellowships
Research grants
Theorems
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2014.0047