Existence of Rational Function

Algebraic Geometry
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Tsakanikas Nickos
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Existence of Rational Function

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Post by Tsakanikas Nickos »

Let $ X $ be a non-singular projective curve and let $ p_{1}, \dots , p_{r} $ be points on $ X $. Show that there exists a non-constant rational function $ f \in K(X) $ which has poles (of some order) at each point $p_{i}$ and which is regular elsewhere.
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