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