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
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.
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.