Abstract
In this paper a proper open holomorphic mapping τ with connected fibres (which are non-singular as analytic sets) of a complex manifold X onto a connected n-dimensional complex manifold Y is investigated. For n>1 there are no isolated critical values, if the groups H2n−1 (FQ;Z) and H2n(FQ;Z) vanish for all Q∈Y, where FQ is the fibre over Q. For n=1 the mapping τ is regular, if all fibres have the same non-vanishing Euler-characteristic. By induction over n it follows that τ is regular, if the groups H2n−1(FQ;Z) and H2n(FQ;Z) vanish for all Q∈Y and all fibres have the same non-vanishing Euler-characteristic.
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Franz, F.H. Über die Menge der kritischen Werte gewisser holomorpher Abbildungen. Manuscripta Math 26, 247–257 (1978). https://doi.org/10.1007/BF01167725
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DOI: https://doi.org/10.1007/BF01167725