English

The cone of moving curves of a smooth Fano-threefold

Algebraic Geometry 2007-05-23 v3

Abstract

In this short note we show that the closed cone of moving curves of a smooth Fano-threefold is polyhedral. The proof relies on a famous result of Bucksom, Demailly, Paun and Peternell which says that the strongly movable cone is dual to the cone of pseudoeffective divisors. Finally, we relate the extremal rays of the cone of moving curves on a threefold with extremal rays in the cone of strongly movable curves on a birational model obtained by a Mori contraction.

Keywords

Cite

@article{arxiv.math/0703025,
  title  = {The cone of moving curves of a smooth Fano-threefold},
  author = {Sammy Barkowski},
  journal= {arXiv preprint arXiv:math/0703025},
  year   = {2007}
}

Comments

12 pages, 1 figure. Version 2: corrected typo in theorem. Version 3: citation added