Exercise 111.34.5 (0297)—The Stacks project

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Exercise 111.34.5. Consider the morphism of schemes

$\pi : X = \mathop{\mathrm{Spec}}(\mathbf{C}[x, y, t] /(1 + t x^3 + t^2 y^3)) \longrightarrow S = \mathop{\mathrm{Spec}}(\mathbf{C}[t])$

Show there does not exist a nonempty open $U \subset S$ and a morphism $\sigma : U \to X$ such that $\pi \circ \sigma = \text{id}_ U$ .

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