Remarks on the normal bundles of generic rational curves (Q1690120)

First the authors gives a different proof of the explicit splitting type of a general degree \(d \geq n\) rational curve in \(\mathbb {P}^n\), \(n\geq 3\), proved in by \textit{G. Sacchiero} [Ann. Univ. Ferrara, Nuova Ser., Sez. VII 26, 33--40 (1980; Zbl 0496.14020)]. They prove that there is a smooth degree \(d\) rational monomial curves with the normal bundle with the generic splitting type if and only if either \(d<3n/2\) or \(d\geq 3n/2\) and \(n\) is odd or \(d\geq 3n/2\), \(n\) is even and \(d = a(n/2) +b\) with \(a\geq 3\) and \(0\leq b \leq (n/2)-a\).