Singular foliations with trivial canonical class

@article{Loray2011SingularFW,
  title={Singular foliations with trivial canonical class},
  author={Frank Loray and Jorge Vit'orio Pereira and Fr'ed'eric Touzet},
  journal={Inventiones mathematicae},
  year={2011},
  volume={213},
  pages={1327-1380}
}
This paper describes the structure of singular codimension one foliations with numerically trivial canonical bundle on complex projective manifolds. 

Tables from this paper

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
On Foliations with Semi-positive Anti-canonical Bundle
  • S. Druel
  • Mathematics
    Bulletin of the Brazilian Mathematical Society, New Series
  • 2018
In this note, we describe the structure of regular foliations with semi-positive anti-canonical bundle on smooth projective varieties.
Codimension 1 Mukai foliations on complex projective manifolds
In this paper we classify codimension 1 Mukai foliations on complex projective manifolds.
Regular foliations on weak Fano manifolds
In this paper we prove that a regular foliation on a complex weak Fano manifold is algebraically integrable.
Codimension one holomorphic foliations on P n : problems in complex geometry
After a short review on foliations, we prove that a codimension 1 holomorphic foliation on P 3 with simple singularities is given by a closed rational 1-form. The proof uses
Codimension One Foliations with Numerically Trivial Canonical Class on Singular Spaces II
In this article, we give the structure of codimension one foliations with canonical singularities and numerically trivial canonical class on varieties with klt singularities. Building on recent
On Fano foliations
In this paper we pursue the study of mildly singular del Pezzo foliations on complex projective manifolds started in [AD13].
Algebraic integrability of foliations with numerically trivial canonical bundle
Given a reflexive sheaf on a mildly singular projective variety, we prove a flatness criterion under certain stability conditions. This implies the algebraicity of leaves for sufficiently stable
Some remarks on regular foliations with numerically trivial canonical class
In this article, we first describe codimension two regular foliations with numerically trivial canonical class on complex projective manifolds whose canonical class is not numerically effective.
Foliations with trivial canonical bundle on Fano 3‐folds
We classify the irreducible components of the space of foliations on Fano 3‐folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 98 REFERENCES
A POSITIVITY PROPERTY FOR FOLIATIONS ON COMPACT KÄHLER MANIFOLDS
We prove that the canonical bundle of a foliation by curves on a compact Kahler manifold is pseudoeffective, unless the foliation is a (special) foliation by rational curves.
Transformation groups of holomorphic foliations
We prove that the self–bimeromorphisms group of a foliation of general type on a projective surface is finite. Along the proof we study the structure of arbitrary codimension foliations on projective
A characterization of diagonal Poisson structures
The degeneracy locus of a generically symplectic Poisson structure on a Fano manifold is always a singular hypersurface. We prove that there exists just one family of generically symplectic Poisson
Bounding the degree of solutions to Pfaff equations
We study hypersurfaces of complex projective manifolds which are invariant by a foliation, or more generally which are solutions to a Pfaff equation. We bound their degree using classical results on
Foliations with trivial canonical bundle on Fano 3‐folds
We classify the irreducible components of the space of foliations on Fano 3‐folds with rank one Picard group. As a corollary we obtain a classification of holomorphic Poisson structures on the same
TRANSVERSELY PROJECTIVE FOLIATIONS ON SURFACES: EXISTENCE OF MINIMAL FORM AND PRESCRIPTION OF MONODROMY
We introduce a notion of minimal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this minimal form exists and is unique when
IRREDUCIBLE COMPONENTS OF THE SPACE OF HOLOMORPHIC FOLIATIONS OF DEGREE TWO IN CP(N), N 3
In this paper we will prove that the space of holomorphic fo- liations of codimension 1 and degree 2 in CP(n), n > 3, has six irreducible components.
Holomorphic symplectic geometry: a problem list
The usual structures of symplectic geometry (symplectic, contact, Poisson) make sense for complex manifolds; they turn out to be quite interesting on projective, or compact Kahler, manifolds. In
On the density of algebraic foliations without algebraic invariant sets
Abstract Let X be a smooth complex projective variety of dimension greater than or equal to 2, L an ample line bundle and k ≫ 0 an integer. We prove that a very generic global section of the twisted
Some Basic Results on Actions of Nonaffine Algebraic Groups
We study actions of connected algebraic groups on normal algebraic varieties, and show how to reduce them to actions of affine subgroups.
...
1
2
3
4
5
...