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The cone of moving curves of a smooth Fano-threefold

Sammy Barkowski
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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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Sammy Barkowski. 2007-04-03. The cone of moving curves of a smooth Fano-threefold. https://arxiv.org/abs/math/0703025

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