A <complex manifold> of complex dimension $n$ is a Hausdorff, second-countable <topological manifold> with charts to open subsets of $\mathbb C^n$ whose transition maps are <biholomorphic>. A rank-$r$ <holomorphic vector bundle> is a complex <vector bundle> with local trivializations $E|_U\cong U\times\mathbb C^r$ whose transition matrices are holomorphic maps to $\operatorname{GL}_r(\mathbb C)$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 118 / 1 / a / Solution

 Solution (source code)