On Factorization of Holomorphic Mappings

K. Stein
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K. Stein: University of Chicago, Department of Mathematics

A chapter in Proceedings of the Conference on Complex Analysis, 1965, pp 1-7 from Springer

Abstract: 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.

Keywords: Holomorphic Mapping; Complex Space; Complex Manifold; Cauchy Integral Formula; Ringed Space (search for similar items in EconPapers)
Date: 1965
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-48016-4_1

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DOI: 10.1007/978-3-642-48016-4_1

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