Exercise 111.34.6 (0298)—The Stacks project

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$X = \mathop{\mathrm{Spec}}(\mathbf{C}[\{ x_ i\} _{i = 1}^{8}, s, t] /(1 + s x_1^3 + s^2 x_2^3 + t x_3^3 + st x_4^3 + s^2t x_5^3 + t^2 x_6^3 + st^2 x_7^3 + s^2t^2 x_8^3))$

and

$S = \mathop{\mathrm{Spec}}(\mathbf{C}[s, t])$

and the morphism of schemes

$\pi : X \longrightarrow S$

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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