# Hyperelliptic Riemann surface and their branch points.

Where can I find (book, notes, ...) the following result:

Theorem: A hyperelliptic Riemann surface $S$ of genus $g$ with two to one map $f: \longrightarrow \mathbb{P}^1$. Then $S$ is determined completely by the $2g + 2$ branch points of $f$.

Thank you!

• I feel like this must be somewhere in Hartshorne chapter IV.. – Tabes Bridges Dec 18 '17 at 18:51
• I can not find :( – Manoel Dec 19 '17 at 19:34