A note on envelopes of holomorphy

Abstract

Let $p:X⟶M$ be a Riemann domain over a connected $n$-dimensional complex submanifold $M$ of ${\mathbb{C}}^N$ and let $\mathcal{F}\subset \mathcal{O}(X)$ be such that $p\in {\mathcal{F}}^N$. Our aim is to discuss relations between the $\mathcal{F}$-envelope of holomorphy of $(X,p)$ in the sense of Riemann domains over $M$ and the $\mathcal{F}$-envelope of holomorphy of $X$ in the sense of complex manifolds.