What is the Ahlfors/Rudin/Lang of several complex variables? Ideally discussing complex manifolds (not just Riemann surfaces) as well.
EDIT: I'd prefer to see a more geometrical than analytical treatment.
Posted Apr 11, 2013, 4:07 AM UTC · edited
Maybe Hörmander's An introduction to complex analysis in several variables.
I've been told that Scheidemann's Introduction to Complex Analysis in several Variables works really well as an introduction, but I think it covers only 'elementary' theory like Hartogs theorems up to Cartan-Thullen and not much material on Stein manifolds.
Griffiths and Harris, "Principles of Algebraic Geometry." Or "Complex Analytic Geometry" by Whitney. Both are glorious. OH, and Griffiths and Adams' book, whose title I can't remember.
It's really neat when you look more into the interplay between complex manifolds and complex analytic varieties. Especially when the varieties are inside some ambient complex manifold, 'cause then you have both the standard topology AND the (analytic) Zariski topology to play with.
-> I'm studying complex analytic geometry in grad school, and these are the books my advisor demands I know.
Analytic Functions of Several Complex Variables, Gunning and Rossi
http://www.amazon.com/Analytic-Functions-Several-Variables-Publishing/dp/0821821652/ref=sr_1_1?s=books&ie=UTF8&qid=1365700922&sr=1-1
Function Theory of Several Complex Variables, Steven Krantz
http://www.amazon.com/Function-Several-Complex-Variables-Publishing/dp/0821827243/ref=pd_sim_b_1