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A remark on separate holomorphy

Marek Jarnicki·Peter Pflug
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Abstract

Let $X$ be a Riemann domain over $\mathbb C^k\times\mathbb C^\ell$. If $X$ is domain of holomorphy with respect to a family $\mathcal F\subset\mathcal O(X)$, then there exists a pluripolar set $P\subset\mathcal C^k$ such that every slice $X_a$ of $X$ with $a\notin P$ is a domain of holomorphy with respect to the family $\{f|_{X_a}: f\in\mathcal F\}$.

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Marek Jarnicki, Peter Pflug. 2005-07-15. A remark on separate holomorphy. https://arxiv.org/abs/math/0507305

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