As one can deduce from the questions I have asked on MO, I'm interested in complex geometry. I am aware that there are many facets to the field, some of which I am more comfortable with than others. This question is about the algebraic aspect of the theory, which is the by far the one I am least familiar with. I am about to start working through the first couple of chapters of Principles of Algebraic Geometry by Griffiths and Harris, but I'm not sure this will contain all the tools I will eventually need.
Which concepts from algebraic geometry does a complex geometer need? Are there any references which do a good job of presenting this material in the setting of complex geometry?
Of course, I would love to learn as much mathematics as possible, in particular, algebraic geometry, but my time is limited, so I have to use it wisely.
