Abstract
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 ϕ : X → X × C l , which are holomorphically trivial. Using this we construct an infinite family { C 2 p + 3 } ( p is a prime number) of complex manifolds, such that every C 2 p + 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.
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