Normal Bundle of Rational Curves and Waring Decomposition

TL;DR

This paper investigates the splitting of the normal bundle of rational space curves and uncovers a novel connection between Waring decomposition of binary forms and the normal bundle's structure.

Contribution

It introduces a new approach to determine the normal bundle splitting for curves in projective spaces of dimension three or higher, linking it to Waring decompositions.

Findings

Results for curves embedded in $bP^m$ for $m \\geq 3$

Establishment of a relationship between Waring decomposition and normal bundle splitting

Extension of classical results from the 1980s

Abstract

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