Normal Bundles of Rational Curves in Projective Spaces

Abstract

We determine the splitting (isomorphism) type of the normal bundle of a generic genus-0 curve with 1 or 2 components in P n , as well as the way the bundle deforms locally with a general deformation of the curve. We deduce an enumerative formula for divisorial loci of smooth rational curves whose normal bundle is of non-generic splitting type.