Rationally connected foliations after Bogomolov and McQuillan

By Stefan Kebekus, L. S. Conde, M. Toma. 2005

82 citations recorded by the source corpus.

This paper is concerned with a sufficient criterion to guarantee that a given foliation on a normal variety has algebraic and rationally connected leaves. Following ideas from a preprint of Bogomolov-McQuillan and using recent works of Langer and Graber-Harris-Starr, we give a clean, short and simple proof of previous results. Apart from a new vanishing theorem for vector bundles in positive characteristic, our proof employs only standard techniques of Mori theory and does not make any reference to the more involved properties of foliations in characteristic p. We apply the result to show that Q-Fano varieties with unstable tangent bundles always admit a sequence of partial rational quotients naturally associated to the Harder-Narasimhan filtration.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1c05be232d6890621926edf05331cf827b9c970e

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In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Foliations with trivial canonical bundle on Fano 3‐folds (2011, background): “5], [21, Chapter 9], which was later generalized by Bogomolov and McQuillan [3], [19].”
Families of canonically polarized varieties over surfaces (2005, background): “6] or [7], asserts that then S is uniruled, leading to a contradiction.”
Singular foliations with trivial canonical class (2011, result): “The result stated below is a particular case of a more general result by Bogomolov and McQuillan proved in [6], see also [29].”