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 Teichmuller family of compact Riemann surfaces, and a theorem of Moisezon 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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