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I have seen the following construction and I would be very happy if someone could explain its meaning to me.

We start from a smooth projective algebraic variety $Z$ over the complex numbers and a reduced effective divisors with simple normal crossings $D$. Let $V=Z-D$. Let $U \to V$ be an étale cover.

What's the meaning of taking $\pi: Y \to X$ the normalization of $Z$ in the function field $\mathbb{C}(U)$?

Does it mean that $U \hookrightarrow Y$ and that the complement is a divisor with normal crossings laying above $D$?

Thanks for your help

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