I am curious to learn about complex manifolds and complex geometry.

I am familiar with the classical algebraic and analytic theory of Riemann surfaces, complex analysis in one variable (say, first nine chapters of R. Narasimhan's book), and basic sheaf theory and cohomology, analytic sheaves and varieties, Chow's theorem and few results in complex analytic geometry here and there. I am comfortable with the theory of smooth real manifolds, but I have minimal background in differential geometry, so a reference to fix that would also be appreciated.

I am looking for a reference that is accessible and fun to read over the long break, given my background; the book by Kodaira felt a bit too advanced for me to try right now.


1 Answer 1



1.You can refer to Complex Geometry written by Daniel Huybrechts.

It is an excellent primer.

2.You can refer to Principal of Algebraic Geometry written by Griffiths and Harris and Complex Analytic and Differential Geometry written by Jean-Pierre Demailly.

They have more differential-geometric points of view.

3.You can refer to Hodge Theory and Complex Algebraic Geometry 1 written by Claire Voisin.

It may be more difficult and advanced and have more algebraic points of view.

Notes and Lectures

1.Notes about complex manifolds which is a wonderful supplement of the Huybrechts' book.


2.New lectures written by Hossein Movasati about the Hodge theory.


3.If you interested in Kahler Manifolds,you can see the lectures written by Werner Ballmann.



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