This paper consists in a revision and extension of a classic result, Waring's Theorem, about the barycenter of the intersection points of two plane algebraic curves. The theorem arises from the study of the parts with highest degree of the equation of a curve, which are completely determined by the barycentric parallel lines of the groups of asymptotes.
"Waring's Theorem revisited." Rocky Mountain J. Math. 49 (3) 979 - 1003, 2019. https://doi.org/10.1216/RMJ-2019-49-3-979