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Codimension One Regular Foliations on Rationally Connected Threefolds

Codimension One Regular Foliations on Rationally Connected Threefolds In his work on birational classification of foliations on projective surfaces, Brunella showed that every regular foliation on a rational surface is algebraically integrable with rational leaves. This led Touzet to conjecture that every regular foliation on a rationally connected manifold is algebraically integrable with rationally connected leaves. Druel proved this conjecture for the case of weak Fano manifolds. In this paper, we extend this result showing that Touzet’s conjecture is true for codimension one foliations on threefolds with nef anti-canonical bundle. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Bulletin of the Brazilian Mathematical Society, New Series" Springer Journals

Codimension One Regular Foliations on Rationally Connected Threefolds

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References (37)

Publisher
Springer Journals
Copyright
Copyright © Sociedade Brasileira de Matemática 2022
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-022-00298-5
Publisher site
See Article on Publisher Site

Abstract

In his work on birational classification of foliations on projective surfaces, Brunella showed that every regular foliation on a rational surface is algebraically integrable with rational leaves. This led Touzet to conjecture that every regular foliation on a rationally connected manifold is algebraically integrable with rationally connected leaves. Druel proved this conjecture for the case of weak Fano manifolds. In this paper, we extend this result showing that Touzet’s conjecture is true for codimension one foliations on threefolds with nef anti-canonical bundle.

Journal

"Bulletin of the Brazilian Mathematical Society, New Series"Springer Journals

Published: Dec 1, 2022

Keywords: Regular foliation; Holomorphic foliation; Foliated MMP; Rationally connected manifolds; Primary 14M22; Secondary 37F75

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