Let $f\colon X\rightarrow Y$ be a dominant, finite, and proper map of normal varieties of degree $d$ over an algebraically closed field $k$. Let $y\in Y$ be any closed point.

**Question.** Is it true that $\# f^{-1}(y)\le d$? (counting points without multiplicity)

Normality of $Y$ is necessary as is shown by the resolution of the nodal cubic. Probably normality of $X$ is unnecessary. This is easy to show in the case of flat maps, but it seems strangely annoying to prove in the case of normal varieties. Ideally, it would be a straightforward application of Zariski's main theorem.

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