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1 vote
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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 …
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 …
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 …