Related papers: Computing basepoints of linear series in the plane
We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is shown, for lengths up to 5.
We compute the equivariant fundamental class of the orbit closure of a linear series on the projective line. We also describe the boundary of the orbit closure and how the orbits specialise in one parameter families.
We show how the computer algebra system OSCAR can be used to obtain topologically correct or visually pleasing drawings of real plane algebraic curves.
In this paper, we present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. That is, we deal with mathematical objects that are assumed to be given approximately. More precisely, given a tolerance…
We define a plane curve to be threadable if it can rigidly pass through a point-hole in a line L without otherwise touching L. Threadable curves are in a sense generalizations of monotone curves. We have two main results. The first is a…
A well-known and difficult problem in computational number theory and algebraic geometry is to write down equations for branched covers of algebraic curves with specified monodromy type. In this article, we present a technique for computing…
Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…
The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…
Given two curves in $\PP^3$, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the…
For affine plane curves defined over the rationals of genus at least two, we show that a decision algorithm for the existence of solutions also yields a search algorithm for all solutions.
Let $\mathcal{F}$ be a plane singular curve defined over a finite field $\mathbb{F}_q$. The linear system of plane curves of a given degree passing through the singularities of $\cF$ provides potentially good bounds for the number of points…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
We consider the open problem of determining the graded Betti numbers for fat point subschemes supported at general points of the projective plane. We relate this problem to the open geometric problem of determining the splitting type of the…
Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for the minimum-weight subset of the obstacles separating the two points.…
We give a closed formula for the dimension of all linear systems in $\mathbb{P}^n$ with assigned multiplicity at arbitrary collections of points lying on a rational normal curve of degree $n$. In particular we give a purely geometric…
A plane curve is a knot diagram in which each crossing is replaced by a 4-valent vertex, and so are dual to a subset of planar quadrangulations. The aim of this paper is to introduce a new tool for sampling diagrams via sampling of plane…
We present a method to detect discontinuity curves, usually called faults, from a set of scattered data. The scheme first extracts from the data set a subset of points close to the faults. This selection is based on an indicator obtained by…
We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. These criteria reduce the projection problem to a certain…
We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also…