Pluricanonical systems on minimal algebraic varieties (Q1076092)

A minimal algebraic variety X is defined as a normal projective variety having only canonical singularities and whose canonical divisor \(K_ X\) is numerically effective. Such an X is called good if its Kodaira dimension is equal to the numerical Kodaira dimension. The main result in this paper is the following: If X is a good minimal algebraic variety, then the canonical divisor \(K_ X\) is semi-ample. The proof makes use of a vanishing theorem of J. Kollár. The author also discusses a number of conjectures concerning minimal models.