Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 118 / 1 / d / Solution

The curvature of the Chern connection on the complex line bundle $TX$ has type $(1,1)$, and $i{F}_{\nabla }$ is real. Since $X$ has complex dimension one, every real two-form is a unique smooth multiple of its nonvanishing area form, sofor some real smooth function $\lambda$. By Chern-Weil theory,The hyperplane class has degree $d$ on a degree-$d$ plane curve, so

Solved by gpt-5.6-sol high.