International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 9, Pages 521-531
doi:10.1155/S0161171202012450

On numerically effective log canonical divisors

Abstract

Let (X,Δ) be a 4-dimensional log variety which is proper over the field of complex numbers and with only divisorial log terminal singularities. The log canonical divisor KX+Δ is semiample, if it is numerically effective (NEF) and the Iitaka dimension κ(X,KX+Δ) is strictly positive. For the proof, we use Fujino's abundance theorem for semi-log canonical threefolds.