On a theorem of Zariski-Van Kampen type and its applications (Q1911584)

Let \(M\) be a complex manifold and let \(\mu:E\to M\) be a holomorphic vector bundle. The author shows a way of relating the fundamental groups \(\pi_1(E-S)\) and \(\pi_1 (M-B)\), where \(S\) is an hypersurface of \(E\) and \(S-\mu^{-1} (B)\to M-B\) is an unbranched covering, provided that there is a section \(\sigma\) with \(\sigma(M)\cap S=\emptyset\). As an application, the author computes the fundamental group of Reg(\(X\)), for some normal hypersurfaces \(X\subset{\mathbb{C}}^n\).