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Complex Analysis and Geometry pp 45–101Cite as

On the Fibers of Analytic Mappings

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Abstract

Let f: X → S be a morphism of complex or real spaces, and P a property of homomorphisms of local rings. Consider the set ℙ(f) of points x∈X for which the induced map of local rings O S,f(x) → O X,x has property P. In this chapter we give a criterion for ℙ(f) being constructible (resp., Zariski open) in X. Moreover, we verify this criterion for a wide class of properties P.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität, D-8400, Regensburg, Germany

    Jürgen Bingener

  2. Mathematisches Institut, Georg-August-Universität, D-3400, Göttingen, Germany

    Hubert Flenner

Authors
  1. Jürgen Bingener
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  2. Hubert Flenner
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Editor information

Editors and Affiliations

  1. Università di Firenze, Florence, Italy

    Vincenzo Ancona

  2. Università di Roma “La Sapienza”, Rome, Italy

    Alessandro Silva

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© 1993 Springer Science+Business Media New York

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Bingener, J., Flenner, H. (1993). On the Fibers of Analytic Mappings. In: Ancona, V., Silva, A. (eds) Complex Analysis and Geometry. The University Series in Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9771-8_2

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  • DOI: https://doi.org/10.1007/978-1-4757-9771-8_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9773-2

  • Online ISBN: 978-1-4757-9771-8

  • eBook Packages: Springer Book Archive

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