On Factorization of Holomorphic Mappings

Abstract

Let X, Y be reduced complex spaces, τ: X → Y a holomorphic mapping, denote by R the equivalence relation in X defined by the level sets (i. e. the connected components of the fibres) of τ. If the level sets are compact then by a theorem of H. Cartan [1] the quotient space X/R carries naturally the structure of a complex space and the natural projection ε: X → X/R is a proper holomorphic mapping; thus τ admits a factorization τ = τ* o ε where τ*: X/R → Y is a nowhere degenerate holomorphic mapping.

Received June 8, 1964.