"Examples in complex geometry."

The algebraic and differential geometry and Hodge theory side of complex geometry is well established in many books, but I've had real trouble finding examples that are worked out in detail (which would be perfect as exercises, perhaps if given with hints) that show how the theory works in practise and provide counterexamples to some implications. For example, an ample line bundle does not have to admit any global sections, but I've never seen an example of such a bundle given in a textbook.