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Smooth contractible hypersurfaces in \(\mathbb{C}^ n\) and exotic algebraic structures on \(\mathbb{C}^ 3\). (English) Zbl 0792.57013

We present new examples of exotic algebraic structures on \(\mathbb{R}^ 6\), i.e., examples of smooth complex affine algebraic manifolds that are diffeomorphic to \(\mathbb{R}^ 6\), but not isomorphic to \(\mathbb{C}^ 3\). These exotic algebraic structures are contractible hypersurfaces in \(\mathbb{C}^ 4\), each of them admits a regular \(\mathbb{C}^*\)-action with one fixed point and they have Kodaira logarithmic dimension 2.
We also present a general method of constructing contractible hypersurfaces in \(\mathbb{C}^ n\) which are not equivalent to a hyperplane up to a polynomial coordinate substitution.
Reviewer: S.Kaliman (Miami)

MSC:

57R40 Embeddings in differential topology
14J70 Hypersurfaces and algebraic geometry
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