Search
Search Results
-
-
Regularity and symbolic defect of points on rational normal curves
In this paper we study ideals of points lying on rational normal curves defined in projective plane and projective 3-space. We give an explicit...
-
Integer Points on Elliptic Curves
This chapter begins with preliminaries on Diophantine equations and Diophantine approximations, which are used later in the chapter. That includes...
-
Parametrization of Algebraic Points of Low Degree on the Hyperelliptic Curves \(y^{2}=x(x^2-n^2)(x^2-4n^2)\)
We give a parametrization of the set of algebraic points of degree at most 3 over...
-
Implicit Representations of Rational Curves and Surfaces
The subject of this chapter is the implicitization of rational algebraic curves and surfaces, that is to say the computation of the image of a curve...
-
-
Recovery of Plane Curves from Branch Points
We recover plane curves from their branch points under projection onto a line. Our focus lies on cubics and quartics. These have 6 and 12 branch...
-
Quadratic points on dynamical modular curves
Among all the dynamical modular curves associated to quadratic polynomial maps, we determine which curves have infinitely many quadratic points. This...
-
Approximation in the Mean on Rational Curves
In the presence of a positive, compactly supported measure on an affine algebraic curve, we relate the density of polynomials in Lebesgue...
-
Real Algebraic Geometry of Real Algebraic Jordan Curves in the Plane and the Bergman Kernel
We characterize the space of restrictions of real rational functions to certain algebraic Jordan curves in the plane via the Dirichlet-to-Neumann map...
-
Detecting Affine Equivalences Between Implicit Planar Algebraic Curves
We present a complete algorithm for computing the affine equivalences between two implicit planar algebraic curves. We provide evidence of the...
-
Approximation in the Mean on Rational Curves
In the presence of a positive, compactly supported measure on an affine algebraic curve, we relate the density of polynomials in Lebesgue
... 
-
Remarks on double points of plane curves
We study the relation between the type of a double point of a plane curve and the curvilinear 0-dimensional subschemes of the curve at the point. An...
-
Number of Limit Cycles for Planar Systems with Invariant Algebraic Curves
For planar polynomials systems the existence of an invariant algebraic curve limits the number of limit cycles not contained in this curve. We...
-
A Numerical Method for Solving Elliptic Equations on Real Closed Algebraic Curves and Surfaces
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite...
