I would like to learn some complex geometry, especially the interaction between algebraic geometry and complex geometry.
I found that there are several famous books:
- Huybrechts, Complex Geometry;
- Voisin, Hodge theory and complex algebraic geometry;
- Griffiths & Harris, Principles of algebraic geometry;
- Demailly, Complex analytic and differential geometry;
- Carlson, Muller-Stach, Peters, Period Mappings and Period Domains;
- Cattani, El Zein, etc., Hodge Theory.
I am not familiar with differential geometry. So I would like to start with the most basic (or self-contained) books, as well as the one can help me understand algebraic geometry. In order to choose the best book for me, I would like to know what these books mainly talk about, difference between them, and the roadmap between these books.
The only thing I know is, according to what Huybrechts said in preface, Voisin and GH's books can be regarded as further readings. However, since I am an entire layman to complex geometry, even after going through the tables of contents of both books, I still don't know if these two books are equivalent, or focus on different topics.
Any comments, reviews, and instruction are welcome! Thanks a lot!