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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.

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    $\begingroup$ I cannot resist: you need to know the Albanese. $\endgroup$ Nov 7, 2014 at 4:22
  • $\begingroup$ Knowing this seems enough www-fourier.ujf-grenoble.fr/~demailly/manuscripts/analmeth.pdf $\endgroup$
    – user40276
    Nov 7, 2014 at 5:14
  • $\begingroup$ Serre's GAGA (Alg.Geom. and Anal.Geom.) would be helpful . A link to an english translation is given in "Serre's FAC in English" (MO-question,answer 2). $\endgroup$
    – Al-Amrani
    Nov 7, 2014 at 15:42

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