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Higher-dimensional foliated Mori theory

Part of: Complex dynamical systems Birational geometry

Published online by Cambridge University Press:  14 November 2019

Calum Spicer
Calum Spicer*
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK email [email protected]
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Abstract

We develop some foundational 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 (MMP) for rank 2 foliations on threefolds.

Keywords

foliationsminimal model programKleiman–Mori conefoliation singularities

MSC classification

Primary: 14E30: Minimal model program (Mori theory, extremal rays) 37F75: Holomorphic foliations and vector fields
Type
Research Article
Information
Compositio Mathematica , Volume 156 , Issue 1 , January 2020 , pp. 1 - 38
Copyright
© The Author 2019 

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Footnotes

1

Current address: Department of Mathematics, King’s College London, London WC2R 2LS, UK

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