For the preparation of a complex geometry lecture I am looking for a good literature. I already have standard literature like Huybrechts "Complex Geometry. An Introduction" and I am also using it. But this book is very "global", in the sense that it only explains the usual quantities (Hermitian metric, Kähler metric, connections, all kinds of curvature, Complex Laplace-Beltrami operator etc.) from a very abstract and formal point of view and it omits local coordinate computation (like writing the Hermitian metric in local coordinates and deriving all kinds of relations between the coefficients ...).
Question: I would like to ask you, if you know any good reference on complex geometry (book, lecture notes, paper, survey etc.) which explains all these complex geometric quantities as mentioned above (Hermitian metric, ...) but from a "local" point of view (in coordinates, deriving all kinds of relation between the coefficients, ...) ?