Related papers: Logarithmic Foliations
The aim of this paper is to describe complex foliations on Kahler surfaces.
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…
We study monodromy groups of elliptic fibrations over the projective line.
We study analytic deformations and unfoldings of holomorphic foliations in complex projective plane $\mathbb{C}P(2)$. Let $\{\mathcal{F}_t\}_{t \in \mathbb{D}_{\epsilon}}$ be topological trivial (in $\mathbb{C}^2$) analytic deformation of a…
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…
Positive geometries encode the physics of scattering amplitudes in flat space-time and the wavefunction of the universe in cosmology for a large class of models. Their unique canonical forms, providing such quantum mechanical observables,…
We present a list of open questions in the theory of holomorphic foliations, possibly with singularities. Some problems have been around for a while, others are very accessible.
We study the relationship between singular holomorphic foliations in $(\mathbb{C}^{2},0)$ and their separatrices. Under mild conditions we describe a complete set of analytic invariants characterizing foliations with quasi-homogeneous…
We study the existence of first integral for holomorphic foliations in different scenarios and under different conditions, for instance germ of foliations given by vector fields and having a formal first integral or infinitely many…
We prove an extension criterion for codimension one foliations on projective hypersurfaces based on the degree of the foliation and the degree of the hypersurface, and we ensure, in some instances, an isomorphism between the corresponding…
This report discusses recent results as well as new perspectives in the ergodic theory for Riemann surface laminations, with an emphasis on singular holomorphic foliations by curves. The central notions of these developments are leafwise…
The purpose of this thesis is to obtain the degree of the exceptional component of the space of holomorphic foliations of degree two and codimension one in P3. I construct a parameter space as an explicit fiber bundle over the variety of…
In this paper we classify codimension 1 Mukai foliations on complex projective manifolds
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…
In this paper, we are interested in flat metric structures with conical singularities on surfaces which are obtained by deforming translation surface structures. The moduli space of such flat metric structures can be viewed as some…
In characteristic zero, we construct principalization of ideals on smooth orbifolds endowed with a normal crossings divisor and a foliation. We then illustrate how the method can be used in the general study of foliations via two…
We introduce an algebraic method for describing the Hodge filtration of degenerating hypersurfaces in projective toric varieties. For this purpose, we show some fundamental properties of logarithmic differential forms on proper equivariant…
Let $X$ a projective manifold equipped with a codimension $1$ (maybe singular) distribution whose conormal sheaf is assumed to be pseudoeffective. By a theorem of Jean-Pierre Demailly, this distribution is actually integrable and thus…
Developing ideas of \cite{Fei}, we introduce canonical cosimplicial cohomology of meromorphic functions for infinite-dimensional Lie algebra formal series with prescribed analytic behavior on domains of a complex manifold $M$. Graded…
In these introductory notes we give the basics of the theory of holomorphic foliations and laminations. The emphasis is on the theory of harmonic currents and unique ergodicity for laminations transversally Lipschitz in CP^2 and for generic…