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On extending regular
holomorphic maps from Stein manifolds
Chester Cornelius Seabury |
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Vol. 65 (1976), No. 2, 499–515
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Abstract |
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In this paper the following results are proved. Theorem. Let S,M be complex manifolds, S a Stein manifold, and f : S → M a holomorphic embedding. Let K ⊂ S be compact, and let Nf be the normal bundle of f. We identify S with the zero section of Nf. Then in Nf, there is a neighborhood U of K, and a holomorphic embedding F : U → M such that F|U ∩ S = f. If f above is an immersion, then there is an immersion F as above. There is also an analogous result for holomorphic maps f which are regular at some point p in S. The idea of the proof is to construct a function ϕ on a neighborhood of f(K) ⊂ M such that ϕ is strictly plurisubharmonic and ϕ−1((−∞,c]) is compact for all c in R. Then a result of Forster and Ramspott is applied to get the final results. To construct ϕ, special coordinates are obtained near f(S) in M. |
Mathematical Subject Classification 2000
Primary: 32C25
Secondary: 32D20
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Milestones
Received: 12 April 1976
Published: 1 August 1976
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Authors |
| Chester Cornelius Seabury | |
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