Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 152 / 2 / a / v / Solution

Part (iii) givestwo complex projective lines meeting at one point. If $x\ne 0$, the fiber ${\mathbb{P}}^1\times \{x\}$ misses the blowup center. The blowup map is an isomorphism of algebraic varieties away from its center, sofor every nonzero closed point $x\in {\mathbb{A}}^1$.