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Über die kritischen Werte gewisser holomorpher Abbildungen

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Abstract

In this note, it is proved that a proper open holomorphic mapping of a three-dimensional complex manifold onto a two-dimensional complex manifold cannot have isolated critical values, if the generic fibre is not the Riemann sphere. The main tools used are the universal property of the Teichmüller family of compact Riemann surfaces, and a theorem of Moišezon asserting that the indeterminacies of certain meromorphic mappings can be resolved by a succession of monoidal transformations with non-singular centres.

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Authors and Affiliations

  1. Universität Regensburg, FB Mathematik, Universitätsstr. 31, 84 Regensburg

    R. R. Simha

  2. School of Mathematics, Tata Institute of Fundamental Research, Bombay 5, India

    R. R. Simha

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  1. R. R. Simha
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Der Referent hat mich darauf aufmerksam gemacht, daß diese Aussage auch bei Brieskorn (Singularitäten von Hyperflächen, Habilitationsschrift, Bonn 1967) bewiesen worden ist.

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Simha, R.R. Über die kritischen Werte gewisser holomorpher Abbildungen. Manuscripta Math 3, 97–104 (1970). https://doi.org/10.1007/BF01168463

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