Global Variants of Hartogs' Theorem

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Date

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24

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Oberwolfach Preprints (OWP)

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Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach

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Abstract

Hartogs' 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.

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