The Stacks project

Exercise 111.55.7. Let $f \in \mathbf{C}[x, y]$ be a nonconstant polynomial. Show that for some $\alpha , \beta \in \mathbf{C}$ the $\mathbf{C}$-algebra map

\[ \mathbf{C}[t] \longrightarrow \mathbf{C}[x, y]/(f),\quad t \longmapsto \alpha x + \beta y \]

is finite.

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View Exercise 111.55.7 as pdf