On the Intersection of Two Plane Curves
نویسنده
چکیده
This problem is related to a conjecture of Kobayashi and Zaidenberg which states that for a sufficiently general curve D ⊂ P of degree d ≥ 5, as general in the sense that D lies in |OP2(d)| ∼= P d(d+3)/2 with countably many closed proper subvarieties removed, the affine variety P\D is hyperbolic. One necessary condition for P\D being hyperbolic is that there is no rational curve C ⊂ P meeting D set-theoretically at fewer than three points; otherwise, there is going to be a nonconstant holomorphic map C → C\(C ∩ D) ⊂ P\D. This property of P\D was called “algebraic hyperbolic” in [DSW].
منابع مشابه
Sink Location Service Based on Fano Plane in Wireless Sensor Networks
Sink location is considered as a basic service in geographic routing in wireless sensor networks. Obtaining the location of sink node by source node using an efficient method with low complexity has always been a challenging issue in research. In this paper, a sink location algorithm based on Fano plane is proposed. The research challenge is how to ensure the intersection of two SLQ (Location Q...
متن کاملComputing quadric surface intersections based on an analysis of plane cubic curves
Computing the intersection curve of two quadrics is a fundamental problem in computer graphics and solid modeling. We present an algebraic method for classifying and parameterizing the intersection curve of two quadric surfaces. The method is based on the observation that the intersection curve of two quadrics is birationally related to a plane cubic curve. In the method this plane cubic curve ...
متن کاملIntersection graphs of curves in the plane
Let V be a set of curves in the plane. The corresponding intersection graph has V as the set of vertices, and two vertices are connected by an edge if and only if the two corresponding curves intersect in the plane. It is shown that the set of intersection graphs of curves in the plane is a proper subset of the set of all undirected graphs. Furthermore, the set of intersection graphs of straigh...
متن کاملTropical Resultants for Curves and Stable Intersection
We introduce the notion of resultant of two planar curves in the tropical geometry framework. We prove that the tropicalization of the algebraic resultant can be used to compute the stable intersection of two tropical plane curves. It is shown that, for two generic preimages of the curves to an algebraic framework, their intersection projects exactly onto the stable intersection of the curves. ...
متن کاملA special subspace of weighted spaces of holomorphic functions on the upper half plane
In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...
متن کاملPlane Algebraic Curves
We go over some of the basics of plane algebraic curves, which are planar curves described as the set of solutions of a polynomial in two variables. We study many basic notions, such as projective space, parametrization, and the intersection of two curves. We end with the group law on the cubic and search for torsion points.
متن کامل