相关论文: The reductivity of spherical curves

In this paper we study the geometry of metric spheres in the curve complex of a surface, with the goal of determining the "average" distance between points on a given sphere. Averaging is not technically possible because metric spheres in…

Given a real algebraic curve in the projective 3-space, its hyperbolicity locus is the set of lines with respect to which the curve is hyperbolic. We give an example of a smooth irreducible curve whose hyperbolicity locus is disconnected…

There are 106 individual types of singular points for reducible complex sextic curves.

We investigate the number of curves having a rational point of almost minimal height in the family of quadratic twists of a given elliptic curve. This problem takes its origin in the work of Hooley, who asked this question in the setting of…

We consider the set E of curves with positive algebraic curvature, whose extremities and tangents in their extremities are given. For each of the curves of E, we define the minimum of the radius of curvature. There exists a unique curve of…

We consider a finite analytic morphism $\varphi =(f,g)$ defined from a complex analytic normal surface $(Z,z)$ to ${\mathbb C}^2$. We describe the topology of the image by $\varphi$ of a reduced curve on $(Z,z)$ by means of iterated pencils…

We estimate the maximal number of integral points which can be on a convex arc in the plane with given length, minimal radius of curvature and initial slope.

We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to configurations of four quadrics admitting a continuum of common tangents. We formulate geometrical conditions in…

We give an explicit construction of a closed curve with constant torsion and everywhere positive curvature. We also discuss the restrictions on closed curves of constant torsion when they are constrained to lie on convex surfaces.

We propose a criterion for examining whether or not the uncertainty of the outer rotation curves is sufficiently small to distinguish a Keplerian rotation curve from flat ones. We have applied this criterion to both Keplerian and…

Every smooth cubic plane curve has 9 flex points and 27 sextatic points. We study the following question asked by Farb: Is it true that the known algebraic structures give all the possible ways to continuously choose $n$ distinct points on…

Let $\Sigma$ be a smooth projective surface, let $f' : S' \to \Sigma$ be a double cover of $\Sigma$ and let $\mu : S \to S'$ be the canonical resolution. Put $f = f'\circ\mu$. An irreducible curve $C$ on $\Sigma$ is said to be a splitting…

When the plane is pie-sliced in $n\leq 4$ parts (with nonempty interior and common vertex at the origin) our main result provides a sufficient condition for any map $L$, that is continuous and piecewise linear relatively to this slicing, to…

Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and…

We prove a lower bound for the topological complexity, in the sense of Smale, of the problem of finding a flex point on a cubic plane curve. The key is to bound the Schwarz genus of a cover associated to this problem. We also show that our…

Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…

In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not…

The aim of this paper is to classify reduction types of algebraic curves. Reduction types capture the discrete invariants of fibres in one-dimensional families of curves, and they have been described in genus 1, 2 and 3. For fixed genus…

It is known for a long time that a nonsingular real algebraic curve of degree 2k in the projective plane cannot have more than 7/2*k^2-9/4*k+3/2$ even ovals. We show here that this upper bound is asymptotically sharp, that is to say we…

A new characterization of rational torsion subgroups of elliptic curves is found, for points of order greater than 4, through the existence of solution for systems of Thue equations.