Asymptotes and centers of affine algebraic curves

Abstract.

In the $18^{{\rm th}}$ and $19^{{\rm th}}$ century many beautiful theorems about the intersection of plane algebraic curves have been discovered. The book of Coolidge [C] contains a large collection of such results. One may ask which of these theorems can be generalized to curves in higher dimensional spaces. In this note we wish to discuss a generalization of a theorem of Waring and apply it to the question which affine algebraic curves have a unique "center".