Non-equivalent embeddings into complex Euclidean spaces

• We study the number of equivalence classes of proper holomorphic embeddings of a Stein space X into C-n. In this paper we prove that if the automorphism. group of X is a Lie group and there exists a proper holomorphic embedding of X into C-n, 0 < dim X < n, then for any k >= 0 there exist uncountably many non-equivalent proper holomorphic embeddings Φ: X x C-k hooked right arrow C-n x C-k. For k = 0 all embeddings will be proved to satisfy the additional property of C-n\Φ)(X) being (n-dim X)-Eisenman hyperbolic. As a corollary we conclude that there are uncountably many non-equivalent proper holomorphic embeddings of C-k into C-n whenever 0 < k < n.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

proper holomorphic embeddings

hyperbolicity

Eisenman

complex analysis

MATHEMATICS

MATEMATIK

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