Genera Of Curves

Algebraic Geometry
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Tsakanikas Nickos
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Genera Of Curves

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Post by Tsakanikas Nickos »

Let $ f \ \colon X \longrightarrow Y $ be a finite morphism between non-singular projective curves over an algebraically closed field $k$. Let $g(X)$ and $g(Y)$ be the genera of $X$ and $Y$, respectively. Show that $g(X) \geq g(Y)$. When does the equality hold?
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