Let $\pi: Y \to X$ be a finite morphism of projective varieties over a field $k$, ramified over a divisor $D \subset X$. Let {$\{ X_t \}$} be a pencil of hyperplane section with respect to some embedding $X \hookrightarrow \mathbb{P}^N$.

**Question.** Is $\pi^{-1}(X_t)$ a pencil of hyperplane sections on $Y$?