Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 146 / 2 / a / Solution

Regard $X={\mathbb{CP}}^2$ as a Kähler manifold with its standard structure, letand choose $ϵ\ne 0$. The smooth conicrepresents $2H=[C_1]+[C_2]$. The standard complex structure is compatible with the Fubini-Study form, and $C_1$, $C_2$, and $\Sigma$ are all its complex submanifolds. It therefore supplies the required example.