相关论文: Double Rational Normal Curves with Linear Syzygies
We relate the equianalytic and the equisingular deformations of a reduced complex plane curve to the Jacobian syzygies of its defining equation. Several examples and conjectures involving rational cuspidal curves are discussed.
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…
For a smooth plane cubic $B$, we count curves $C$ of degree $d$ such that the normalizations of $C\backslash B$ are isomorphic to $\Bbb A^1$, for $d\leq7$ (for $d=7$ under some assumption). We also count plane rational quartic curves…
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
Consider the scheme parametrizing non-constant morphisms from a fixed projective curve to a projective surface. There is a rational map between this scheme and the Chow variety of $1$-cycles on the surface. We prove that, if the curve is…
We study a particular plane curve over a finite field whose normalization is of genus 0. The number of rational points of this curve achieves the Aubry-Perret bound for rational curves. The configuration of its rational points and a…
This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…
A system of plane curves defined by prescribing n points of multiplicity m in general position is regular if n > (2m)^2. The proof uses computation of limits of linear systems acquiring fixed divisors, an interesting problem in itself.
The present paper is a natural continuation of a previous work where we studied the second syzygy scheme of canonical curves. We find sufficient conditions ensuring that the second syzygy scheme of a genus--$g$ curve of degree at least…
We consider the curves whose all normal planes are at the same distance from a fixed point and obtain some characterizations of them in the 3-dimensional Euclidean space.
A rational triangle is a triangle with rational side lengths. We consider three different families of rational triangles having a fixed side and whose vertices are rational points in the plane. We display a one-to-one correspondence between…
We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature. We also establish the fundamental theorem of existence in…
Rational double points are the simplest surface singularities. In this essay we will be mainly concerned with the geometry of the exceptional set corresponding to the resolution of a rational double point. We will derive the classification…
This article aims to extend classical homological results about the rational normal curves to analogues in weighted projective spaces. Results include determinantality and nonstandard versions of quadratic generation and the Koszul…
We give several constructions of bicuspidal rational complex projective plane curves, and list the Newton pairs and the multiplicity sequences of the singularities on the resulting curves. Although the existence of some of the listed cusp…
We investigate the duality between local (complex analytic) projective structures on surfaces and two dimensional (complex analytic) neighborhoods of rational curves having self-intersection +1. We study the analytic classification,…
One distinguishing feature of rational curves is that they have algebraic parameterizations. Arc spaces are a way of describing approximations to parameterizations of all curves in some fixed space. Playing on these descriptions, this paper…
In this paper, we consider rational cuspidal plane curves having exactly two cusps whose complements have logarithmic Kodaira dimension two. We classify such curves with the property that the strict transforms of them via the minimal…