Exercise 111.34.6. Consider the schemes
\[ X = \mathop{\mathrm{Spec}}(\mathbf{C}[\{ x_ i\} _{i = 1}^{8}, s, t] /(1 + s x_1^3 + s^2 x_2^3 + t x_3^3 + st x_4^3 + s^2t x_5^3 + t^2 x_6^3 + st^2 x_7^3 + s^2t^2 x_8^3)) \]
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 $\pi \circ \sigma = \text{id}_ U$.
Comments (0)
There are also: