A remark on separate holomorphy
Volume 174 / 2006
Studia Mathematica 174 (2006), 309-317
MSC: 32D05, 32D25.
DOI: 10.4064/sm174-3-5
Abstract
Let $X$ be a Riemann domain over ${\mathbb C}^k\times{\mathbb C}^\ell$. If $X$ is a domain of holomorphy with respect to a family ${\mathcal F}\subset{\mathcal O}(X)$, then there exists a pluripolar set $P\subset{\mathbb C}^k$ such that every slice $X_a$ of $X$ with $a\notin P$ is a region of holomorphy with respect to the family $\{f|_{X_a}: f\in{\mathcal F}\}$.
