Abstract
It is proved that a proper holomorphic mapping f f between bounded complete Reinhardt domains extends holomorphically past the boundary and that if, in addition, f − 1 ( 0 ) = { 0 } {f^{ - 1}}(0) = \{ 0\} , then f f is a polynomial mapping. The proof is accomplished via a transformation rule for the Bergman kernel function under proper holomorphic mappings.
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