# Tagged Questions

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### Linear systems and 2-torsion shifts on hyperelliptic curves

Let $C$ be a hyperelliptic curve of genus $g$ and let $D$ be a divisor on $C$ of degree $g+1$. Assume that the linear system $|D|$ is base-point-free. Now add a $2$-torsion point $[E]$ to $D$. I would ...
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### Finding functions on curves with given multiplicity at a point

just migrated these questions from SE, I hope is ok. Let $C/k$ be a smooth curve over a field (not necessarily perfect) , $P\in C(k)$ and $n\in \mathbb{Z}^{+}$ such that $n>1$ I want to find a ...
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### About the characteristic polynomial of Frobenius of the Jacobian of a genus 2 hyperelliptic curve

I was looking for some information related to the values of the characteristic polynomial $\chi(t)$ of the Frobenius of a Jacobian of a hyperelliptic curve $C$ of genus 2 over $\mathbb{F}_q$ and in ...
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### Curves of higher genus

I saw the question: Abelian varieties with CM and though I know that there are rare CM elliptic curves, I wonder what kind of curves with higher genus have the CM Jacobians?
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### How order of divisor with support at infinity is changed at reduction?

Jing Yu in his paper "On Arithmetic Of Hyperelliptic Curves" on page 5 asserts the following The most interesting case is certainly the case $k = \mathbb Q$ and $D \in \mathbb Z[t]$. To ...
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### Abelian varieties with CM

In this site, I looked at a paper of Kazuma Morita claiming the BSD conjecture for the CM case posted on his homepage (he made a mistake three years ago for full BSD). But, I am interested in this ...
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### Easiest example where field of definition is not field of moduli

There are many examples of varieties over $\overline{\mathbb Q}$ whose field of moduli is $\mathbb Q$ but which can't be defined over $\mathbb Q$. What is the easiest such example? It should be a ...
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### Equivalent binary forms

Two binary forms $f, g \in k[x, y]$ are equivalent when there exists an $M \in GL_2 (k)$ such that $f^M = g$. For simplicity we take $k$ such that $char (k) =0$ and $k=\bar k$. The equivalence ...
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