The Stacks project

Exercise 111.39.4. Show there does not exist a nonconstant morphism of schemes $\mathbf{P}^2_{\mathbf{C}} \to \mathbf{P}^1_{\mathbf{C}}$ over $\mathop{\mathrm{Spec}}(\mathbf{C})$. Here a constant morphism is one whose image is a single point. (Hint: If the morphism is not constant consider the fibres over $0$ and $\infty $ and argue that they have to meet to get a contradiction.)

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View Exercise 111.39.4 as pdf