The cone of moving curves of a smooth Fano-threefold

2007/03/01 by Sammy Barkowski, Barkowski, Sammy
Mathematics · #14E30 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E30

paper · pdf · doi:10.48550/arxiv.math/0703025

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

arxiv created 2007/04/03 · arxiv updated 2009/12/01

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.

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