Title: Implicitization of Parameterized Curve and the intersection problem by means of matrix representation
Abstract : Let f0,f1,...,fn be n homogeneous polynomials in K[s,t] of the same positive degree d without common factor. The image of the rational map
from the projective line to the n-projective space sending (s:t) to (f0:f1:...:fn)(s,t), is an algebraic curve C.
A matrix M with entries in K[x0,x1,...,xn] is said to be a representation of a given rational space curve C if
M is generically full rank and if the rank of M drops exactly on C.
At first, we present how to obtain new matrix representations of rational parameterized curves. And after, we
develop the curve/curve intersection problem in the n-projective space which are motivated by
recent research in this topic.
