Zbigniew Jelonek: Exotic embeddings of smooth affine varieties

We find examples of exotic embeddings of smooth affine varieties into
C^n in large codimensions.  We show also examples of affine smooth,
rational algebraic varieties X, for which there are algebraically
exotic embeddings \phi : X -> X x C which are holomorphically
trivial. Using this we construct an infinite family $\{{\cal
C}_{2p+3}\}$ (p is a prime number) of complex manifolds, such that
every ${\cal C}_{2p+3}$ has at least two different algebraic
(quasi-affine) structures.  We show also that there is a natural
connection between Abhyankar-Sathaye Conjecture and the famous
Quillen-Suslin Theorem.