Normal Bundle of Rational Curves and Waring Decomposition

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

Cited by in corpus (2)

• Strata of vector spaces of forms in k[x,y] and of rational curves in P^k
• PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle