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Francesco Polizzi
Francesco Polizzi
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Given a curve $X$$C$, does there exist a rational function on $X$$C$ totally ramified at two given points?

Let $X$$C$ be a smooth projective irreducible curve over $\mathbb C$. Let $x$ and $y$ be distinct points of $C$.

We say that $f$ is totally ramified at a point $P$$p$ if the ramification index of $P$$p$ equals $\deg(f)$.

Does $X$$C$ admit a finite map $f:X\to \mathbb P^1$$f \colon C \to \mathbb P^1$ which is totally ramified at $x$ and $y$?

Given a curve $X$, does there exist a rational function on $X$ totally ramified at two given points

Let $X$ be a smooth projective irreducible curve over $\mathbb C$. Let $x$ and $y$ be distinct points.

We say that $f$ is totally ramified at a point $P$ if the ramification index of $P$ equals $\deg(f)$.

Does $X$ admit a finite map $f:X\to \mathbb P^1$ which is totally ramified at $x$ and $y$?

Given a curve $C$, does there exist a rational function on $C$ totally ramified at two given points?

Let $C$ be a smooth projective irreducible curve over $\mathbb C$. Let $x$ and $y$ be distinct points of $C$.

We say that $f$ is totally ramified at a point $p$ if the ramification index of $p$ equals $\deg(f)$.

Does $C$ admit a finite map $f \colon C \to \mathbb P^1$ which is totally ramified at $x$ and $y$?

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Marc E
Marc E
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Given a curve $X$, does there exist a rational function on $X$ totally ramified at two given points

Let $X$ be a smooth projective irreducible curve over $\mathbb C$. Let $x$ and $y$ be distinct points.

We say that $f$ is totally ramified at a point $P$ if the ramification index of $P$ equals $\deg(f)$.

Does $X$ admit a finite map $f:X\to \mathbb P^1$ which is totally ramified at $x$ and $y$?