Answer by Maarten Derickx for Hyperelliptic modular curves in characteristic p
I already gave the currently accepted answer to this question around 10 years ago. And the answer can be summarised as "Yes, here is an example". However, after 10 years I wanted to come back to this...
View ArticleAnswer by Maarten Derickx for Hyperelliptic modular curves in characteristic p
A curve $C$ is hyperelliptic if and only if the canonical map $C \to \mathbb P^*(\Omega^1(C))$, which sends a point $p$ to the codimension 1 subspace $V_p \subset\Omega^1(C)$ of all one forms vanishing...
View ArticleAnswer by JSE for Hyperelliptic modular curves in characteristic p
This is sort of a cheap answer, but I would look at values of N where X_0(N) has genus 3 and is not hyperelliptic (over Q). In genus 3, the locus of hyperelliptic curves has codimension 1 in the whole...
View ArticleHyperelliptic modular curves in characteristic p
Ogg characterized the finitely many N such that $X_0(N)_{\mathbb{Q}}$ is hyperelliptic, and Poonen proved in "Gonality of modular curves in characteristic p" that for large enough N,...
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