Hello
I am trying to get a good book that explains the Dolbeault Cohomology, does anyone know of a good one?
Hello I am trying to get a good book that explains the Dolbeault Cohomology, does anyone know of a good one? 


Chern's book "Complex manifolds without potential theory" is a good book, and it does explain Dolbeault Cohomology. But it's a short book, and it explains it concisely. If you need more details, you could also try GriffithsHarris (but I greatly prefer Chern's book). Kodaira's book "Complex manifolds and deformations of complex structures" is much more leisurely, and with great attention paid to exposition and detail (it doesn't appeal to some people, but I enjoyed it a lot). 


I like "Hodge Theory and Complex Algebraic Geometry" by Voisin. The focus is on the Kahler case, but the early explanations of Dolbeaut cohomology are for all complex manifolds. 


If I remember right there should be something in "Differential Analysis on Complex Manifolds" by Wells. 


Another book that covers Dolbeault cohomology very nicely is "Complex Geometry" by Daniel Huybrechts. I highly recommend it. 


Chapter 0.2 of Griffith and Harris 


The references given in the wikipedia article . 

