Related papers: Complete Algebraic Vector Fields on Danielewski Su…
A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector fields. They model a number of geometric and physical…
We study algebraic integrability of complex planar polynomial vector fields $X=A (x,y)(\partial/\partial x) + B(x,y) (\partial/\partial y) $ through extensions to Hirzebruch surfaces. Using these extensions, each vector field $X$ determines…
In this paper we study exponential maps ($\mathbb{G}_a$-actions) on the family of affine two dimensional surfaces of the form $f(x)y=\phi(x,z)$ over arbitrary fields, describe the Makar-Limanov invariant and Derksen invariant of these…
This paper investigates the geometry of smooth canonically polarized surfaces defined over a field of positive characteristic which have a nontrivial global vector field, and the implications that the existence of such surfaces has in the…
Finite-dimensional subalgebras of a Lie algebra of smooth vector fields on a circle, as well as piecewise-smooth global transformations of a circle on itself, are considered. A canonical forms of realizations of two- and three-dimensional…
The aim of this work is focused on the investigation of the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra $a_4^{(2)}$. First, we prove that the generic fiber of the momentum map for this…
We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the…
We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is…
Given a fibration of a symplectic manifold by lagrangian tori, we show that each symplectic vector field splits into two parts : the first is Hamiltonian and the second is symplectic and preserves the fibration. We then show an application…
We consider a construction of observables by using methods of supersymmetric field theories. In particular, we give an extension of AKSZ-type observables using the Batalin-Vilkovisky structure of AKSZ theories to a formal global version…
We characterize contractible curves on proper normal algebraic surfaces in terms of complementary Weil divisors. Using this we generalize the classical criteria of Castelnuovo and Artin. As application we derive a finiteness result on…
We consider the Zariski-Lipman Conjecture on free module of derivations for algebraic surfaces. Using the theory of non-complete algebraic surfaces, and some basic results about ruled surfaces, we will prove the conjecture for several…
In this article, we study various concrete algebraic and differential geometric properties of the Cartwright-Steger surface. In particular, we determine the genus of a generic fiber of the Albanese fibration, and deduce that the singular…
Suppose V is a surface over a number field k that admits two elliptic fibrations. We show that for each integer d there exists an explicitly computable closed subset Z of V, not equal to V, such that for each field extension K of k of…
The sl_2-triples play a fundamental role for the structure theory of Lie algebras, and representation theory in general. Here we investigate sl_2-triples of global vector fields on schemes X in positive characteristics p>0, and develop a…
We study the cohomological equation for a smooth vector field on a compact manifold. We show that if the vector field is cohomology free, then it can be embedded continuously in a linear flow on an Abelian group.
In this paper, we explore the structure of the Hitchin map for higher dimensional varieties with emphasis on the case of algebraic surfaces.
We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional manifold have geodesible vector fields.
In this paper we address the following questions: (i) Let $C\subset \mathbb C^2$ be an orbit of a polynomial vector field which has finite total Gaussian curvature. Is $C$ contained in an algebraic curve? (ii) What can be said of a…
This paper gives a classification of the topology of vector fields which are nowhere tangent to the fibers of a Seifert fibering.