Genera Of Curves
Posted: Thu Jun 16, 2016 9:45 pm
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?