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If $X\subset\mathbb{P}^n$ is a hyperplane, what is the function field $K(X)$ ? Is $K(X)$ just k?

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A hyperplane is isomorphic to $\mathbb{P}^{n-1}$. Do you know what the function field of $\mathbb{P}^{n-1}$ is? – Qiaochu Yuan Nov 29 '12 at 0:55

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