Related papers: Polar foliations on symmetric spaces

In this short note we study foliations with rationally connected leaves on surfaces. Our main result is that on surfaces there exists a polarisation such that the Harder-Narasimhan filtration of the tangent bundle with respect to this…

In the moduli space of polarized varieties the same unpolarized variety can occur multiple times However, for K3 surfaces, compact hyperk\"ahler manifolds, and abelian varieties the number is finite. This may be viewed as a consequence of…

Polar spaces over finite fields are fundamental in combinatorial geometry. The concept of polar space was firstly introduced by F. Veldkamp who gave a system of 10 axioms in the spirit of Universal Algebra. Later the axioms were simplified…

Deformation of morphisms along leaves of foliations define the tangential foliation on the corresponding space of morphisms. We prove that codimension one fo-liations having a tangential foliation with at least one non-algebraic leaf are…

We give a short proof of the contractibility of the space of geodesic triangulations with fixed combinatorial type of a convex polygon in the Euclidean plane. Moreover, for any $n>0$, we show that there exists a space of geodesic…

We produce examples of codimension one foliations of the Euclidean and hyperbolic planes with bounded geometry which are topologically products, but for which leaves are non-recursively distorted. That is, the function which compares…

A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

We classify polar actions on complex hyperbolic spaces up to orbit equivalence.

We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space $\mathscr F_q(r, d)$ of singular foliations of codimension $q$ and degree $d$ on the complex…

The space of codimension one holomorphic foliations of degree 1 in a projective space has an irreducible component whose general element is a logarithmic differential 1-form with simple poles in three hyperplanes. We compute its projective…

We prove that the moduli space A_3(1,1,4) of polarized abelian threefolds with polarization of type (1,1,4) is unirational. By a result of Birkenhake and Lange this implies the unirationality of the isomorphic moduli space A_3(1,4,4). The…

We present a variant of the classical Darboux-Jouanolou Theorem. Our main result provides a characterization of foliations which are pull-backs of foliations on surfaces by rational maps. As an application, we provide a structure theorem…

This article studies codimension one foliations on projective man-ifolds having a compact leaf (free of singularities). It explores the interplay between Ueda theory (order of flatness of the normal bundle) and the holo-nomy representation…

This work explores the space of foliations on projective spaces over algebraically closed fields of positive characteristic, with a particular focus on the codimension one case. It describes how the irreducible components of these spaces…

After a short review on foliations, we prove that a codimension 1 holomorphic foliation on $\mathbb P^3_{\mathbb C}$ with simple singularities is given by a closed rational 1-form. The proof uses Hironaka-Matsumura prolongation theorem of…

We give a necessary and sufficient condition for orbits of commutative Hermann actions and actions of the direct product of two symmetric subgroups on compact Lie groups to be biharmonic in terms of symmetric triad with multiplicities. By…

We investigate the degree of the polar transformations associated to a certain class of multi-valued homogeneous functions. In particular we prove that the degree of the pre-image of generic linear spaces by a polar transformation…

The notion of a complex hyperpolar action on a symmetric space of non-compact type has recently been introduced as counterpart of a hyperpolar action on a symmetric space of compact type. In this paper, we construct examples of a complex…

A finite classical polar space of rank $n$ consists of the totally isotropic subspaces of a finite vector space over $\mathbb{F}_q$ equipped with a nondegenerate form such that $n$ is the maximal dimension of such a subspace. A…

By making use of the classification of real simple Lie algebra, we get the maximum of the squared length of restricted roots case by case, thus we get the upper bounds of sectional curvature for irreducible Riemannian symmetric spaces of…