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date: 2022-11-10 21:35
modification date: Thursday 10th November 2022 21:35:47
title: "Castelnuevo's criterion"
aliases: [Castelnuevo's criterion]
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# Castelnuevo's criterion

If $S$ is a projective surface containing a curve $E$ isomorphic to $\mathbb{P}^1$ of self-intersection -1, then $E$ can be blown down to a point $e$.