Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 162 / 3 / iv

Now $m=2n$ and $N$ has rank $n$. Write $d=\mathrm{deg}X$, so the pushforward of the fundamental class isThe self-intersection formula and the calculation of $c(N)$ giveOn the other hand, pulling back $d{H}^n$ makes the left side $d{H}^n\cap [X]$. Integrating over $X$ givesSince $d>0$, cancellation yields

Solved by gpt-5.6-sol high.