Related papers: Feuilletage lisse de $S^5$ par surfaces complexes
The configuration space of $n$ marked points on the complex plane is considered. We investigate a decomposition of this space by so-called Gauss-skizze i.e. a class of graphs being forests, introduced by Gauss. It is proved that this…
Gay and Kirby introduced the notion of a trisection of a smooth 4-manifold, which is a decomposition of the 4-manifold into three elementary pieces. Rubinstein and Tillmann later extended this idea to construct multisections of…
We define a class of nonsingular holomorphic foliations on compact complex tori which generalizes (in higher codimension) the turbulent foliations of codimension one constructed by Ghys. For those smooth turbulent foliations we prove that…
We describe a family of locally conformal Kaehler metrics on class 1 Hopf surfaces H containing some recent metrics constructed by P. Gauduchon and L. ornea. We study some canonical foliations associated to these metrics, in particular a…
We prove that a logarithmic foliation corresponding to a generic line arrangement of $d+1 \geq 3$ lines in the complex plane, with pairwise natural and co-prime residues, is a smooth point of the center set of plane foliations (vector…
We show that the total space of the Milnor fibration associated with any cusp or simple elliptic singularity in complex three variables admits an $S^1$-parametric genus-one Lefschetz fibration structure over the $2$-disk. As a consequence,…
In this paper we deal with Seifert fibre spaces, which are compact 3-manifolds admitting a foliation by circles. We give a combinatorial description for these manifolds in all the possible cases: orientable, non-orientable, closed, with…
A leafwise Hodge decomposition was proved by Sanguiao for Riemannian foliations of bounded geometry. Its proof is explained again in terms of our study of bounded geometry for Riemannian foliations. It is used to associate smoothing…
This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same $T/I$ class. It is a generalization of the well known \"Ottingen-Riemann torus for triads of…
In this article, we show that for any deformation of analytic foliations, there exists a maximal analytic singular foliation on the space of parameters along the leaves of which the deformation is integrable.
We consider 5-dimensional Lie groups with left-invariant Riemannian metrics. For such groups we give a partial classification of left-invariant conformal foliations with minimal leaves of codimension 2. These foliations produce local…
In arXiv1312.7267, the first non-trivial example of a Poisson manifold of strong compact type is given. The construction uses the theory of K3 surfaces and results in a Poisson manifold with leaf space $S^1$. We modify the construction to…
A smooth foliation is Riemannian when its leaves are locally equidistant. The closures of the leaves of a Riemannian foliation on a simply connected manifold, or more generally of a Killing foliation, are described by flows of transverse…
A way to characterize the space of leaves of a foliation in terms of connections is proposed. A particular example of vertex algebra cohomology of codimension one foliations on complex curves is considered.
The geometric and algebraic properties of smooth projective varieties with 1-regular structure sheaf are well understood, and the complete classification of these varieties is a classical result. The aim of this paper is to study the next…
This is the first in a series of papers about foliations in derived geometry. After introducing derived foliations on arbitrary derived stacks, we concentrate on quasi-smooth and rigid derived foliations on smooth complex algebraic…
Consider a complex analytic manifold $X$ and a coherent Lie subalgebra $\shi$ of the Lie algebra of complex vector fields on $X$. By using a natural $\shd_X$-module $\shm_\shi$ naturally associated to $\shi$ and the ring (in the derived…
R. Zimmer proved that, on a compact manifold, a foliation with a dense leaf, a suitable leafwise Riemannian symmetric metric and a transverse Lie structure has arithmetic holonomy group. In this work we improve such result for totally…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
The paper is a continuation of the authors' work in which we considered foliations formed by the maximal dimensional K-orbits ($MD_5$-foliations) of connected $MD_5$-groups such that their Lie algebras have 4-dimensional commutative derived…