Higher dimensional foliated Mori theory

Abstract

We develop some basic results in a higher dimensional foliated Mori theory, and show how these results can be used to prove a structure theorem for the Kleiman-Mori cone of curves in terms of the numerical properties of $K_{\mathcal{F}}$ for rank 2 foliations on threefolds. We also make progress toward realizing a minimal model program for rank 2 foliations on threefolds.

50 pages, new version taking into account referee suggestions, published version to appear in Compositio Math

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