On Numerically Effective Log Canonical Divisors

Abstract

Let $(X,\Delta )$ 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 $K_X+\Delta$ is semi-ample, if it is nef (numerically effective) and the Iitaka dimension $\kappa (X,K_X+\Delta )$ is strictly positive. For the proof, we use Fujino's abundance theorem for semi log canonical threefolds.

arXiv comment11 pages, AMSTex v2.1, the published version