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Results tagged with hyperelliptic-curves
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user 127343
2
votes
1
answer
209
views
Hyperelliptic equation on a function field
Let us consider a hyperelliptic equation
$$Y^2=A_nX^n+A_{n-1}X^{n-1}+\dots+A_0$$
where $A_i\in\mathbb{C}[z]$. I am interested in rational solutions $X,Y\in\mathbb{C}(z)$ when genus is $\geq 2$ and equ …
- 231
1
vote
0
answers
74
views
Morphisms from plane curves to hyperelliptic curves
Consider a plane curve $\mathcal{C}$ of degree $d$. We know that if a morphism $\varphi$ from $\mathcal{C}$ to a curve of genus $g\geq 2$ exists, then $\deg \varphi \leq (g'-1)/(g-1)$ where $g'$ is th …
- 231
7
votes
1
answer
269
views
Elliptic factors in the Jacobian and zeta function
Consider a hyperelliptic curve $\mathcal{C}$ over $\mathbb{Q}$ and its Jacobian $J(\mathcal{C})$. Assume that $J(\mathcal{C})$ admits an elliptic factor $\mathcal{E}$.
For almost all primes, we can re …
- 231