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On foliations with nef anti-canonical bundle


Author: Stéphane Druel
Journal: Trans. Amer. Math. Soc. 369 (2017), 7765-7787
MSC (2010): Primary 37F75
DOI: https://doi.org/10.1090/tran/6873
Published electronically: May 1, 2017
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Abstract: In this paper we prove that the anti-canonical bundle of a holomorphic foliation $ \mathscr {F}$ on a complex projective manifold cannot be nef and big if either $ \mathscr {F}$ is regular, or $ \mathscr {F}$ has a compact leaf. Then we address codimension one regular foliations whose anti-canonical bundle is nef with maximal Kodaira dimension.


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Additional Information

Stéphane Druel
Affiliation: Institut Fourier, UMR 5582 du CNRS, Université Grenoble 1, BP 74, 38402 Saint Martin d’Hères, France
Email: stephane.druel@univ-grenoble-alpes.fr

DOI: https://doi.org/10.1090/tran/6873
Received by editor(s): July 9, 2015
Received by editor(s) in revised form: November 17, 2015
Published electronically: May 1, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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