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 ${\text{bbP}}^m$ for $m\ge 3$ and we find an interesting interplay between the Waring decomposition of binary forms and the splitting of the normal bundle.