An extension theorem for normal functions

Abstract

Given a domain Ω ⊂ C n \Omega \subset {{\mathbf {C}}^n} , an analytic subvariety V V of Ω \Omega and a normal function f : Ω ∖ V → C ^ f:\Omega \backslash V \to \widehat {\mathbf {C}} , we show that f f can be extended to a holomorphic mapping f ∗ : Ω → C ^ {f^*}:\Omega \to \widehat {\mathbf {C}} provided the singularities of V V are normal crossings.