On the numerical dimension of pseudo-effective divisors in positive characteristic

2012/06/27 by Cascini, Paolo, Hacon, Christopher, Mustata, Mircea +1 · 1 citation
#14E99 (Primary) 13A35 #14F18 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1206.6521

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.

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