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We study complex analytic (possibly singular) projective connections on the plane. We characterize some of them in terms of their families of integral curves. We also give a beginning of classification of second order odes polynomial in the…

Differential Geometry · Mathematics 2023-01-12 Oumar Wone

The purpose of this paper is to study transport equations on the unit tangent bundle of closed oriented Riemannian surfaces and to connect these to the transport twistor space of the surface (a complex surface naturally tailored to the…

Differential Geometry · Mathematics 2024-01-29 Jan Bohr , Thibault Lefeuvre , Gabriel P. Paternain

For $m\in \IN, m\geq 1,$ we determine the irreducible components of the $m-th$ jet scheme of a toric surface $S.$ For $m$ big enough, we connect the number of a class of these irreducible components to the number of exceptional divisors on…

Algebraic Geometry · Mathematics 2010-12-14 Hussein Mourtada

The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic…

Classical Analysis and ODEs · Mathematics 2013-12-17 Thomas Kecker

This paper investigates existence results for path-dependent differential equations driven by a H{\"o}lder function where the integrals are understood in the Young sense. The two main results are proved via an application of Schauder…

Probability · Mathematics 2016-10-28 Rafael Andretto Castrequini , Francesco Russo

Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic description of quantum mechanics, are used to construct time-correlation functions in an initial value representation (IVR). The formulation is fully quantum…

Quantum Physics · Physics 2009-11-10 Eric R. Bittner

The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup-Kupershmidt hierarchy is constructed. The integration of…

Differential Geometry · Mathematics 2012-05-25 Emilio Musso

Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that…

Algebraic Geometry · Mathematics 2022-05-06 Sergey Gaifullin , Georgiy Shirinkin

We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…

Number Theory · Mathematics 2018-12-31 Johannes Schleischitz

We present a method for calculating the Brauer group of a surface given by a diagonal equation in the projective space. For diagonal quartic surfaces with coefficients in Q we determine the Brauer groups over Q and Q(i).

Algebraic Geometry · Mathematics 2023-05-22 Damián Gvirtz-Chen , Alexei N. Skorobogatov

We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…

Differential Geometry · Mathematics 2020-03-25 Yoshiki Matsushita , Takuya Nakashima , Keisuke Teramoto

The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…

Optics · Physics 2009-11-10 Jose B. Almeida

We study rotational surfaces in Euclidean 3-space whose Gauss curvature is given as a prescribed function of its Gauss map. By means of a phase plane analysis and under mild assumptions on the prescribed function, we generalize the…

Differential Geometry · Mathematics 2022-01-19 Antonio Bueno , Irene Ortiz

Two dimensional flows on fixed smooth surfaces have been studied in the point of view of vorticity dynamics. Firstly, the related deformation theory including kinematics and kinetics is developed. Secondly, some primary relations in…

Fluid Dynamics · Physics 2013-04-19 Xi-Lin Xie

We study the number of distinct ways in which a smooth projective surface $X$ can be realized as a smooth toroidal compactification of a ball quotient. It follows from work of Hirzebruch that there are infinitely many distinct ball…

Algebraic Geometry · Mathematics 2015-10-22 Luca F. Di Cerbo , Matthew Stover

We prove a conjecture of Barraud-Cornea for orientable Lagrangian surfaces. As a corollary, we obtain that displaceable Lagrangian 2--tori have finite Gromov width. In order to do so, we adapt the pearl complex of Biran-Cornea to the…

Symplectic Geometry · Mathematics 2016-01-20 François Charette

We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…

Classical Analysis and ODEs · Mathematics 2013-12-06 Armengol Gasull , Anna Geyer

We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very compact form for normal crossing spaces. The main approach is…

Algebraic Geometry · Mathematics 2023-06-22 Simon Felten , Matej Filip , Helge Ruddat

Let B be the Bergman projection associated to a domain on which the dbar-Neumann operator is compact. We show that arbitrary L^2 derivatives of Bf are controlled by derivatives of f taken in a single, distinguished direction. As a…

Complex Variables · Mathematics 2012-09-26 A. -K. Herbig , J. D. McNeal

We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be equivalent to determining the Mordell-Weil rank of an…

alg-geom · Mathematics 2008-02-03 Peter F. Stiller
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