Normal bundles of rational curves inP 3

LetP ^r=P _k ^r be the projective space over an algebraically closed ground field k. Let X be a rational space cur ve of degree n with only ordinary singularities. Since X is rational, the normal bundleN of X inP ³ splits inN = _{1 2} where ₁, and ₂ are line bundles, and we have deg ₁ + deg ₂ = 4n – 2. We consider the non-negative integer defined by 2 = |deg ₁ – deg ₂|. The aim of this paper is to determine all possible values of and to describe the variety parametrizing all twisted rational curves inP ³ with only ordinary singularities for a fixed degree n and fixed .The paper was supported by C.N.R., while both authors were members of GNSAGA