We introduce an l-adic algorithm to efficiently determine the group of rational torsion points on an elliptic curve. We also make a conjecture about the discriminant of the m-division polynomial of an elliptic curve.

In this paper, the technique of foliations in characteristic p is used to investigate the difference between rational connectedness and separable rational connectedness in positive characteristic. The notion of being freely rationally connected is defined; a variety is freely rationally connected if a general pair of points can be connected by a free rational curve. It is proved that a freely r...

We give a closed formula for the dimension of all linear systems in Pn with assigned multiplicity at arbitrary collections points lying on rational normal curve degree n. In particular we purely geometric explanation speciality these systems, which is due to presence certain subvarieties base locus: spans points, secant varieties or joins between them.

We look at arithmetic progressions on elliptic curves known as Huff curves. By an arithmetic progression on an elliptic curve, we mean that either the x or y-coordinates of a sequence of rational points on the curve form an arithmetic progression. Previous work has found arithmetic progressions on Weierstrass curves, quartic curves, Edwards curves, and genus 2 curves. We find an infinite number...

This paper adresses the problem of least-square fitting with rational pole curves. The issue is to minimize a sum of squared Euclidean norms with respect to three types of unknowns: the control points, the node values, and the weights. A new iterative algorithm is proposed to solve this problem. The method alternates between three steps to converge towards a solution. One step uses the projecti...