Related papers: Derived Foliations
Let $X$ be a connected non-compact $2$-dimensional manifold possibly with boundary and $\Delta$ be a foliation on $X$ such that each leaf $\omega\in\Delta$ is homeomorphic to $\mathbb{R}$ and has a trivially foliated neighborhood. Such…
We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic…
We consider contact foliations: objects which generalise to higher dimensions the flow of the Reeb vector field on contact manifolds. We list a number of properties of such foliations, and propose two conjectures about the topological types…
This article deals with the irreducible components of the space of codimension one foliations in a projective space defined by logarithmic forms of a certain degree. We study the geometry of the natural parametrization of the logarithmic…
This paper explores the sheaves with the action of a lie algebra and computes their cohomology in a new category. Then in the following sections, We try to generalize a classical result in [GM, Ch. IV] about exterior algebra. We add the…
We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of several existing categorical structures for differentiation,…
The connection between the theory of permutation orbifolds, covering surfaces and uniformization is investigated, and the higher genus partition functions of an arbitrary permutation orbifold are expressed in terms of those of the original…
We classify singular foliations admitting a given leaf and a given transverse singular foliation.
The questions of global topological, smooth and holomorphic classifications of the differential systems, defined by covering foliations, are considered. The received results are applied to nonautonomous linear differential systems and…
These notes are a slightly enlarged version of my habilitation thesis, where our research interest and main results in the past few years are summarized. Most of the discussion revolves around complex ordinary differential equations and…
We call a foliation $\mathcal{F}$ on a compact manifold infinitesimally rigid if its deformation cohomology $H^{1}(\mathcal{F},N\mathcal{F})$ vanishes. This paper studies infinitesimal rigidity for a distinguished class of Riemannian…
We trace derivations through Demazure's correspondence between a finitely generated positively graded normal $k$-algebras $A$ and normal projective $k$-varieties $X$ equipped with an ample $\mathbb{Q}$-Cartier $\mathbb{Q}$-divisor $D$. We…
In this paper we investigate homologically finite-dimensional objects in the derived category of a given small dg-enhanced triangulated category. Using these we define reflexivity, hfd-closedness, and the Gorenstein property for…
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…
A semiholomorphic foliations of type (n, d) is a differentiable real manifold X of dimension 2n + d, foliated by complex leaves of complex dimension n. In the present work, we introduce an appropriate notion of pseudoconvexity (and…
These are lecture notes of a course given in Pisa, SNS, in february 2002. They provide a classification of holomorphic foliations of nongeneral type on compact Kaehler surfaces.
Let $\Gamma$ be a finite group acting linearly on a vector space $V$. We compute the Lie algebra cohomology of the Lie algebra of $\Gamma$-invariant formal vector fields on $V$. We use this computation to define characteristic classes for…
Our constructions provide a systematic way to study cohomology pre-algebraic structures via classical cohomology, simplifying computations and enabling the use of established techniques.
In this note, we discuss the interactions between differential topology and isoparametric foliations, surveying some recent progress and open problems.
There exists a smooth foliation with 3 singular points on the two-dimensional torus such that any lifting of a leaf of this foliation on the universal covering of the torus is a dense subset of the covering.