Complex Manifold Basic Books

1k Views Asked by At

I have studied Manifold Theory form the book by Boothby. Now I want to study Theory of Complex Manifolds. But I am a novice in this field. Can anyone suggest me a basic book on the subject?

1

There are 1 best solutions below

1
On

Follow Abel's motto: Read The Masters!
Since Kodaira and Grauert are among the undisputed masters in complex manifold theory, I recommend:
A) Complex Manifolds and Deformation of Complex Structures
B) From Holomorphic Functions to Complex Manifolds

The Kodaira book A) is chock-full of examples. You should essentially begin by studying them, which means reading from page 28 to page 59.
The Fritzsche-Grauert book B) is very rich but you should jump as soon as possible to Chapter IV, pages 153 to 171, which are essentially self-contained.

There are many other books on complex manifolds/varieties/several complex variables : Grauert-Remmert, Gunning-Rossi, Hörmander, Huybrechts, Krantz, Narasimhan, Shabat, Taylor, Wells,.. but none is (in my opinion) more accessible than the above two.