A characterization of semiampleness and contractions of relative curves

Mathematics – Algebraic Geometry

Scientific paper

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6 pages. Minor changes. To appear in Kodai Math. J

Scientific paper

A line bundle with a base-point-free multiple is called semiample. I give a
cohomological characterization of semiample line bundles. The result is a
common generalization of the Fujita-Zariski criterion for semiampleness and the
Grothendieck-Serre characterization of ampleness. Applying the Fujita-Zariski
Theorem, I characterize contractible curves in 1-dimensional families.

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