When studying branched coverings $$f \colon X \to Y$$ of projective manifolds of degree $d$, one may discuss ampleness of the associated vector bundle $\mathcal{E}$ defined by $f_*\mathcal{O}_X = \mathcal{O}_Y \oplus \mathcal{E}^*$ dependent on $Y$. One main consequence of positivity of $\mathcal{E}$ is a Barth-Lefschetz type theorem that yields an isomorphism of cohomology groups $$f^*\colon H^*(Y,\mathbb{C}) \to H^*(X,\mathbb{C})$$ for suitable cohomology groups dependent on the degree $d$ and the dimension of $X$ and $Y$. $f^*$ denotes the pullback map.
My Question is: What are consequences of the Barth-Lefschetz type theorem? What are (minimal) examples of an application?
Thanks in advance.