Systems of polynomial equations defining hyperelliptic d-osculating covers

N-covers of Hyperelliptic Curves

For a hyperelliptic curve C of genus g with a divisor class of order n = g + 1, we shall consider an associated covering collection of curves Dδ , each of genus g2. We describe, up to isogeny, the Jacobian of each Dδ via a map from Dδ to C, and two independent maps from Dδ to a curve of genus g(g − 1)/2. For some curves, this allows covering techniques that depend on arithmetic data of number f...

Coupled systems of equations with entire and polynomial functions

We consider the coupled system$F(x,y)=G(x,y)=0$,where$$F(x, y)=bs 0 {m_1}   A_k(y)x^{m_1-k}mbox{ and } G(x, y)=bs 0 {m_2} B_k(y)x^{m_2-k}$$with entire functions $A_k(y), B_k(y)$.We    derive a priory estimates  for the sums of the rootsof the considered system andfor the counting function of  roots.

Solving Systems of Polynomial Equations

Estimating Differential Quantities using Polynomial fitting of Osculating Jets

This paper addresses the pointwise estimation of differential properties of a smooth manifold S —a curve in the plane or a surface in 3D— assuming a point cloud sampled over S is provided. The method consists of fitting the local representation of the manifold using a jet, and either interpolation or approximation. A jet is a truncated Taylor expansion, and the incentive for using jets is that ...

On the equations defining curves in a polynomial algebra

Let A be a commutative Noetherian ring of dimension n (n ≥ 3). Let I be a local complete intersection ideal in A[T ] of height n. Suppose I/I is free A[T ]/I-module of rank n and (A[T ]/I) is torsion inK0(A[T ]). It is proved in this paper that I is a set theoretic complete intersection ideal in A[T ] if one of the following conditions holds: (1) n ≥ 5, odd; (2) n is even, and A contains the fi...