Pluricanonical systems on minimal algebraic varieties. (English) Zbl 0593.14010

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.
Reviewer: L.D.Olson


14E30 Minimal model program (Mori theory, extremal rays)
14C20 Divisors, linear systems, invertible sheaves
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
Full Text: DOI EuDML


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