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A characterization of semiampleness and contractions of relative curves

Stefan Schroeer
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Abstract

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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Stefan Schroeer. 2001-04-21. A characterization of semiampleness and contractions of relative curves. https://arxiv.org/abs/math/0001183

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