Normal bundle of rational curves and Waring decomposition

The problem of determining the splitting of the normal bundle of rational space curves has been considered in the 80s in a series of papers by Ghione and Sacchiero and by Eisenbud and Van de Ven. With our approach we are able to obtain results for curves embedded in Pm for m⩾3 and we find an interesting interplay between the Waring decomposition of binary forms and the splitting of the normal bundle.