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Complete intersections in Stein manifolds

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Abstract

The purpose of this note is to prove some theorems on set theoretic complete intersections in Stein manifolds (or Stein spaces) which are analogous to results in affine algebraic geometry. Due to the Oka principle in Stein theory one gets stronger results. For example any locally complete intersection Y of dimension ≦3 in a Stein space X with dim X>2 dim Y is a set theoretic6 complete intersection. A 4-dimensional submanifold ofℂ6 is a set theoretic complete intersection if sc 21 (Y)=0 for some integer s>0.

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Authors and Affiliations

  1. Institutul de Matematica, INCREST, Bd. Pacii 220, R-79622, Bucuresti, Romania

    C. Bănică

  2. Mathematisches Institut der Universität, Einstenstr. 64, D-4400, Münster, Federal Republic of Germany

    O. Forster

Authors
  1. C. Bănică
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  2. O. Forster
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Der erstgenannte Autor dankt der Alexander-von-Humboldt-Stiftung für ein Stipendium zu einem Gastaufenthalt an der Universität Münster

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Bănică, C., Forster, O. Complete intersections in Stein manifolds. Manuscripta Math 37, 343–356 (1982). https://doi.org/10.1007/BF01166226

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  • DOI: https://doi.org/10.1007/BF01166226

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