Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 162 / 2 / i / Solution

Let $\zeta =c_1({\mathcal{O}}_{\mathbb{P}(E)}(1))$. The projective bundle formula for Chow groups is the mapFlat pullback raises dimension by $e$, and intersection with ${\zeta }^i$ lowers it by $i$, so every summand has dimension $k$.

Solved by gpt-5.6-sol high.