• Corpus ID: 239024387

Codimension one regular foliations on rationally connected threefolds

@inproceedings{Figueredo2021CodimensionOR,
  title={Codimension one regular foliations on rationally connected threefolds},
  author={Joao Paulo Figueredo},
  year={2021}
}
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… 

References

SHOWING 1-10 OF 36 REFERENCES
On Fano foliations
In this paper we address Fano foliations on complex projective varieties. These are foliations whose anti-canonical class is ample. We focus our attention on a special class of Fano foliations,
MMP for co-rank one foliations on threefolds
We prove existence of flips, special termination, the base point free theorem and, in the case of log general type, the existence of minimal models for F-dlt foliated log pairs of co-rank one on a
Families of rationally connected varieties
Recall that a proper variety X is said to be rationally connected if two general points p, q ∈ X are contained in the image of a map g : P → X. This is clearly a birationally invariant property. When
On the isotriviality of families of elliptic surfaces
We study non-isotrivial projective families of elliptic surfaces of Kodaira dimension one, over complex projective curves. If the base is an elliptic curve, we show that the family must have a
Higher-dimensional foliated Mori theory
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
Codimension 1 foliations with numerically trivial canonical class on singular spaces
In this article, we describe the structure of codimension one foliations with canonical singularities and numerically trivial canonical class on varieties with terminal singularities, extending a
Threefolds whose canonical bundles are not numerically effective.
  • S. Mori
  • Mathematics, Medicine
    Proceedings of the National Academy of Sciences of the United States of America
  • 1980
TLDR
A characterization of an arbitrary nonsingular projective 3-fold whose canonical bundle is not numerically effective and which contains an exceptional divisor of several types, which is classified explicitly.
Canonical Models of Foliations
Thirty years after its publication, it remains true that the only absolutely satisfactory theorem on families of curves on surfaces (so a fortiori on higher dimensional) varieties of general type is
Birational Geometry of Foliations
Introduction: From Surfaces to Foliations.- Local Theory.- Foliations and Line Bundles.- Index Theorems.- Some Special Foliations.- Minimal Models.- Global 1-forms and Vector Fields.- The Rationality
Local and global applications of the Minimal Model Program for co-rank one foliations on threefolds
We show that the Minimal Model Program for co-rank one foliations on threefolds terminates by proving foliation flips terminate. Moreover, we recover a full suite of powerful results on the
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