Related papers: Codimension one foliations with numerically trivia…

We consider singular foliations of codimension one on 3-manifolds, in the sense defined by A. Haefliger as being Gamma_1-structures. We prove that under the obvious linear embedding condition, they are Gamma_1-homotopic to a regular…

We prove that a Morse type codimension one holomorphic foliation is not transverse to a sphere in the complex affine space. Also we characterize the variety of contacts of a linear foliation with concentric spheres.

In this paper, we will construct a pre-normal form for germs of codimension one holomorphic foliation having a particular type of separatrix, of cuspidal type. We will also give a sufficient condition, in the quasi-homogeneous,…

We study the class of compact K\"ahler manifolds with trivial canonical bundle and the property that the cohomology of the trivial line bundle is generated by one element. If the square of the generator is zero, we get the class of strict…

We classify the canonical threefold singularities that allow an effective two-torus action. This extends classification results of Mori on terminal threefold singularities and of Ishida and Iwashita on toric canonical threefold…

We study codimension one foliations in projective space \PP^n over \CC by looking at its first order perturbations: unfoldings and deformations. We give special attention to foliations of rational and logarithmic type. For a differential…

We present existence results for certain singular 2-dimensional foliations on 4-manifolds. The singularities can be chosen to be simple, e.g. the same as those that appear in Lefschetz pencils. There seems to be a wealth of such creatures…

This paper is devoted to the resolution of singularities of holomorphic vector fields and of one-dimensional holomorphic foliations in dimension 3 and it has two main objectives. First, from the general perspective of one-dimensional…

In this paper, we construct counterexamples to the boundedness of generalised log canonical models of surfaces with fixed appropriate invariants, where the underlying varieties can have arbitrary Kodaira dimension. This answers a question…

We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by…

We classify singular fibres of a projective Lagrangian fibration over codimension one points. As an application, we obtain a canonical bundle formula for a projective Lagrangian fibration over a smooth manifold.

We show that a singular Riemannian foliation of codimension two on a compact simply-connected Riemannian $(n+2)$-manifold, with regular leaves homeomorphic to the $n$-torus, is given by a smooth effective $n$-torus action. This solves in…

We investigate the structure of smooth holomorphic foliations with numerically flat tangent bundles on compact K\"ahler manifolds. Extending earlier results on non-uniruled projective manifolds by the second and fourth authors, we show that…

Let G be a simple Lie group of real rank one, and S the ideal boundary of the corresponding symmetric space of noncompact type (H^n_R, H^n_C, H^n_H or H^2_O). We show the finiteness of the possible values of the secondary characteristic…

We study the topology of the space of smooth codimension one foliations on a closed 3-manifold. We regard this space as the space of integrable plane fields included in the space of all smooth plane fields. It has been known since the late…

We describe the valuations following infinitely near singular points of a (singular) holomorphic foliation in the complex plane. They appear to be those satisfying a generalization of L'Hopital's rule. With them, we characterize dicritical…

We study foliations $\mathcal{F}$ on Hirzebruch surfaces $S_\delta$ and prove that, similarly to those on the projective plane, any $\mathcal{F}$ can be represented by a bi-homogeneous polynomial affine $1$-form. In case $\mathcal{F}$ has…

Contents 1. Algebraicity criterion: statement 2. Proof of the algebraicity criterion. 3. Pseudoeffectivity and movable classes. 4. Harder-Narasimhan filtrations and pseudo-effectivity. 5. Pseudo-effectivity of relative canonical bundles. 6.…

The classifying spaces of cobordisms of singular maps have two fairly different constructions. We expose a homotopy theoretical connection between them. As a corollary we show that the classifying spaces in some cases have a simple product…

In the paper we introduce the notions of a singular fibration and a singular Seifert fibration. These notions are natural generalizations of the notion of a locally trivial fibration to the category of stratified pseudomanifolds. For…