In a <holomorphic coordinate> chart, $T^{1,0}X$ has frame $\partial/\partial z^1,\ldots,\partial/\partial z^n$. Under a holomorphic coordinate change $w=w(z)$, the <chain rule> gives
$$
\frac{\partial}{\partial z^j}=\sum_k\frac{\partial w^k}{\partial z^j}\frac{\partial}{\partial w^k}.
$$
The Jacobian is an invertible matrix of <holomorphic functions>. These frames therefore make $T^{1,0}X$ the <holomorphic tangent bundle>.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-118/1/b/solution