Non straightenable complex lines in C2
Abhyankar and Mob, in [1, (1.6), p. 151], and M. Suzuki, in [11, w proved that if P is a polynomial embedding of C into C 2, then there exists ~b, a polynomial automorphism of C 2, such that (~boP)(C)=C x {0}. The corresponding and much easier result has been proved for polynomial embeddings of C into C '~, for n > 4 by Z. Jelonek [7] (more generally, Jelonek treats the case of embeddings of C k into C ~, for n > 2 k + 2 ) . The case of polynomial embeddings of C into C 3 seems open. See also [8]. The main goal of this paper is to show that the above results do not generalize to holomorphic embeddings of C. Another goal is an interpolation theorem (Proposition 2 below).