English

A characterization of semiampleness and contractions of relative curves

Algebraic Geometry 2007-05-23 v2

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.

Keywords

Cite

@article{arxiv.math/0001183,
  title  = {A characterization of semiampleness and contractions of relative curves},
  author = {Stefan Schroeer},
  journal= {arXiv preprint arXiv:math/0001183},
  year   = {2007}
}

Comments

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