## 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

### MSC:

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

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