Related papers: Foliation adjunction
This article presents some computations for a new topological invariant for foliations introduced some years ago by the author using techniques from noncommutative geometry, in particular the pairing between K-Theory and cyclic cohomology.…
In this paper, we study the adjoint foliated structures of the form $K_{\mathcal{F}}+D$ on algebraic surfaces, with particular focus on their minimal and canonical models. We investigate the effective behavior of the multiple linear system…
Every singular foliation has an associated topological groupoid, called holonomy groupoid (see arXiv:math/0612370). In this note we exhibit some functorial properties of this assignment: if a foliated manifold $(M,\mathcal{F}_M)$ is the…
Adjoint functor theorems give necessary and sufficient conditions for a functor to admit an adjoint. In this paper we prove general adjoint functor theorems for functors between $\infty$-categories. One of our main results is an…
In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation…
In this article, we verify the additivity for rank of a sum of coprime monomials and bivariate polynomials generalizing the result in (\cite{CCG}). We also show similar results hold for cactus rank.
We record an explicit proof of the theorem that lifts a two-variable adjunction to the arrow categories of its domains.
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 study foliations $\mathscr{F}$ on projective complete intersection K3 surfaces $X \hookrightarrow \mathbb{P}^n$, where $\mathscr{F}$ has isolated singularities and it is the restriction of a foliation of degree $d$ on $\mathbb{P}^n$ that…
We consider all connected and simply connected 7-dimensional Lie groups whose Lie algebras have nilradical $\g_{5,2} = \s \{X_1, X_2, X_3, X_4, X_5 \colon [X_1, X_2] = X_4, [X_1, X_3] = X_5\}$ of Dixmier. First, we give a geometric…
Combinatoric formulas for cluster expansions have been improved many times over the years. Here we develop some new combinatoric proofs and extensions of the tree formulas of Brydges and Kennedy, and test them on a series of pedagogical…
We prove localization and integration formulas for the equivariant basic cohomology of Riemannian foliations. As a corollary we obtain a Duistermaat-Heckman theorem for transversely symplectic foliations.
We review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities…
Using the theory of Klyachko filtrations for reflexive sheaves on toric varieties, we give a description of toric foliations and their singularities in terms of combinatorial data. We extend Spicer's results about co-rank one toric…
We prove that Riemannian foliations on complete contractible manifolds have a closed leaf, and that all leaves are closed if one closed leaf has a finitely generated fundamental group. Under additional topological or geometric assumptions…
We consider resolution of singularities for $1$-foliations on varieties of dimension at most three in positive characteristic. We prove that such singularities can be completely resolved if we allow tame regular Deligne--Mumford stacks as…
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
The present article is a study of germs of regular foliations transverse to an embedded strongly exceptional submanifold of a complex manifold. Cohomological conditions are given on this embedding for the existence of these foliations and…
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…
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…