Related papers: On First Integrals for Holomorphic Vector Fields
This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is…
We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by the similar property of the fundamental group of the complement of na irreducible hypersurface in the complex projective…
We investigate resolutions of heterotic orbifolds using toric geometry. Our starting point is provided by the recently constructed heterotic models on explicit blowup of C^n/Z_n singularities. We show that the values of the relevant…
We classify nonsingular holomorphic foliations of dimension and codimension one on certain Hopf manifolds. More general, we prove that all nonsingular codimension one distributions on intermediary or generic Hopf manifolds are integrable…
We consider a moduli space of lattice polarized K3 surfaces with the additional information of a frame of the trascendental cohomology with respect to the lattice polarization. This moduli space is proved to be quasi-affine, and the…
We characterize all logarithmic, holomorphic vector-valued modular forms which can be analytically continued to a region strictly larger than the upper half-plane.
The vector field problem is an important and classical problem in differential topology. In this survey we shall consider the vector field problem focusing mainly on the class of compact homogeneous spaces.
For any closed analytic set X in C^2 there exists a proper holomorphic embedding of the unit disk into C^2 such that the image avoids X.
In this paper, we examine some geometric vector fields on 2-step nilmanifolds of dimension 5.
We propose a contour integral representation for the one-point correlators at genus one of the primaries of a family of rational logarithmic conformal field theories.
We discuss the notions of indices of vector fields and 1-forms and their generalizations to singular varieties and varieties with actions of finite groups, as well as indices of collections of vector fields and 1-forms.
We consider complex rational vector fields that admit a first integral whose logarithmic derivative lies in a finite extension of the rational function field $K$. In view of the Prelle-Singer theorem, these are the rational vector fields…
We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity…
Let $\Sigma$ be an open Riemann surface and $Hol (\Sigma)$ be the Lie algebra of holomorphic vector fields on $\Sigma.$ We fix a projective structure (i.e. a local $SL_2(C)-$structure) on $\Sigma.$ We calculate the first group of cohomology…
A Lie algebra structure on variation vector fields along an immersed curve in a $2$-dimensional real space form is investigated. This Lie algebra particularized to plane curves is the cornerstone in order to define a Hamiltonian structure…
We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discrete analogs of completely integrable transformation on closed…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
The main result of this paper is the computation of the Lie superalgebras of holomorphic vector fields on the complex $\Pi$-symmetric flag supermanifolds, introduced by Yu.I.~Manin. We prove that with one exception any vector field is…
In this paper, we characterize conformal vector fields of any (regular or singular) $(\alpha,\beta)$-space with some PDEs. Further, we show some properties of conformal vector fields of a class of singular $(\alpha,\beta)$-spaces satisfying…
On the basis of the canonical quantization procedure of a system defined on a cubic lattice, we propose a new method, in which resolutions of unity expressed in terms of eigenvectors are naturally provided, to find eigenvectors of field…