International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 9, Pages 521-531

On numerically effective log canonical divisors

Shigetaka Fukuda

Faculty of Education, Gifu Shotoku Gakuen University, Yanaizu-Cho, Gifu 501-6194, Japan

Received 18 March 2001; Revised 9 October 2001

Copyright © 2002 Shigetaka Fukuda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.