I'm far from having read all of Hartshorne, but if I did I would study Compact Complex Surfaces, by Bart, Peters, Van de Ven. Also Geometric Invariant Theory would be a nice topic (I know about the book by Mumford, are there other good books on this topic?).

Ah, I forgot! How about derived categories? Someone suggested that for this topic a good reference is the book by Hartshorne "Residues and duality". I had a look at some notes by Caldararu on the arxiv, "Derived categories of sheaves: a skimming", they seem well written.

I'm far from having read all of Hartshorne, but if I did I would study Compact Complex Surfaces, by Barth, Peters, Van de Ven. Also Geometric Invariant Theory would be a nice topic (I know about the book by Mumford, are there other good books on this topic?).

Ah, I forgot! How about derived categories? Someone suggested that for this topic a good reference is the book by Hartshorne Residues and duality. I had a look at some notes by Caldararu on the arxiv, "Derived categories of sheaves: a skimming", they seem well written.

I'm far from having read all of Hartshorne, but if I did I would study Compact Complex Surfaces, by Bart, Peters, Van de Ven. Also Geometric Invariant Theory would be a nice topic (I know about the book by Mumford, are there other good books on this topic?).

I'm far from having read all of Hartshorne, but if I did I would study Compact Complex Surfaces, by Bart, Peters, Van de Ven. Also Geometric Invariant Theory would be a nice topic (I know about the book by Mumford, are there other good books on this topic?).

Ah, I forgot! How about derived categories? Someone suggested that for this topic a good reference is the book by Hartshorne "Residues and duality". I had a look at some notes by Caldararu on the arxiv, "Derived categories of sheaves: a skimming", they seem well written.