Related papers: On closed currents invariant by holomorphic foliat…
We prove that a Morse-Smale gradient-like flow on a closed manifold has a "system of compatible invariant stable foliations" that is analogous to the object introduced by Palis and Smale in their proof of the structural stability of…
We prove that every homogeneous flow on a finite-volume homogeneous manifold has countably many independent invariant distributions unless it is conjugate to a linear flow on a torus. We also prove that the same conclusion holds for every…
Using the method of moving frames we analyze the algebra of differential invariants for surfaces in three-dimensional affine geometry. For elliptic, hyperbolic, and parabolic points, we show that if the algebra of differential invariants is…
We study analytic deformations of holomorphic foliations given by homogeneous integrable one-forms in the complex affine space $\mathbb C^n$. The deformation is supposed to be of first order (order one in the parameter). We also assume that…
We consider closed and orientable immersed hypersurfaces of translational manifolds. Given a vector field on such a hypersurface, we define a perturbation of its Gauss map, which allows us to obtain topological invariants for the immersion…
Inspired by Le Calvez' theory of transverse foliations for dynamical systems of surfaces, we introduce a dynamical invariant, denoted by N, for Hamiltonians of any surface other than the sphere. When the surface is the plane or is closed…
Pursuing McQuillan's philosophy in proving the Green-Griffiths conjecture for certain surfaces of general type, we deal with the algebraic degeneracy of entire curves tangent to holomorphic foliations by curves. Inspired by the recent work…
For an orientable surface with an area form, there are two invariants of area-preserving dynamics, the flux homomorphism and the Calabi invariant. Tsuboi found a remarkable connection between the Calabi invariant on the closed disk and a…
The purpose of this paper is to study singular holomorphic foliations of arbitrary codimension defined by logarithmic forms on projective spaces.
The goal of this paper is to construct invariant dynamical objects for a (not necessarily invertible) smooth self map of a compact manifold. We prove a result that takes advantage of differences in rates of expansion in the terms of a sheaf…
We give a classification of pairs (F, f) where F is a holomorphic foliation on a projective surface and f is a non-invertible dominant rational map preserving F. We prove that both the map and the foliation are integrable in a suitable…
A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve, such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant rational cohomology in…
We prove that the space of coinvariants of functions on an affine variety by a Lie algebra of vector fields whose flow generates finitely many leaves is finite-dimensional. Cases of the theorem include Poisson (or more generally Jacobi)…
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.
Twisted supersymmetric theories on a product of two Riemann surfaces possess non-local holomorphic currents in a BRST cohomology. The holomorphic currents act as vector fields on the chiral ring. The OPE's of these currents are invariant…
In this work, we begin by showing that a holomorphic foliation with singularities is reduced if and only if its normal sheaf is torsion free. In addition, when the codimension of the singular locus is at least two, it is shown that being…
We prove that a transversely holomorphic foliation which is transverse to the fibers of a fibration, is a Seifert fibration if the set of compact leaves is not of zero measure. Similarly, we prove that a finitely generated subgroup of…
In this paper, we address one of the most basic and fundamental problems in the theory of foliations and ODEs, the topological invariance of the algebraic multiplicity of a holomorphic foliation. For instance, we prove an adapted version of…
In this paper we explore the general conditions in order that a 2-dimensional natural Hamiltonian system possess a second invariant which is a polynomial in the momenta and is therefore Liouville integrable. We examine the possibility that…
Let f be a non-invertible holomorphic endomorphism of a projective space and f^n its iterate of order n. We prove that the pull-back by f^n of a generic (in the Zariski sense) hypersurface, properly normalized, converge to the Green current…