# algebraic map of projective smooth plane curves

Let $f: C \rightarrow C$ ' be a non-constant algebraic map of projective smooth plane curves. Show that $g(C) \geq g(C$ '$)$, where g(.) denotes the genus.

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Apply Hurwitz's theorem. –  Andrea May 20 '12 at 21:17
there are different types of hurwitz theorem, which one do we need to use ? Can you please be more specific. Thanks –  user22170 May 20 '12 at 21:26
Corollary IV.2.4 of Hartshorne. –  Andrea May 20 '12 at 21:35