(A related question is this On the fundamental group of hypersurfaces).

Let $X$ be a simply connected projective complex manifold of dimension at least 3. Let $Y\subset X$ be a smooth hypersurface. What is $\pi_1(Y)$ then? If $Y$ is a hyperplane section, then $\pi_2(X,Y)=0$ by the Lefschetz theorem, hence $\pi_1(Y)=0$. The question is, can we say anything about the fundamental group of a hypersurface without assuming ampleness?