Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Bochnak, JacekKucharz, Wojciech2024-10-162024-10-162018https://oa.tib.eu/renate/handle/123456789/16887https://doi.org/10.34657/15909Hartogs' theorem asserts that a separately holomorphic function, defined on an open subset of Cⁿ, is holomorphic in all the variables. We prove a global variant of this theorem for functions defined on an open subset of the product of complex algebraic manifolds. We also obtain global Hartogs-type theorems for complex Nash functions and complex regular functions.eng510Separately holomorphicHartog's theoremComplex algebraic manifoldGlobal Hartog's theoremNash functionRegular functionReport