Let $f:X\to Y$ be a non-constant morphism of smooth projective connected curves over $\mathbf{C}$ (or compact connected Riemann surfaces).
Suppose that $X=Y$ and that $f$ is not the identity.
Why are the fixed points of $f$ isolated?
Let $f:X\to Y$ be a non-constant morphism of smooth projective connected curves over $\mathbf{C}$ (or compact connected Riemann surfaces).
Suppose that $X=Y$ and that $f$ is not the identity.
Why are the fixed points of $f$ isolated?