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Could any one tell me name of some books on several complex variable for some one who will start reading the subject for the first time in his life. he has back ground on Differential geometry,complex analysis one variable, algebraic topology,commutative algebra.

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marked as duplicate by Amzoti, Dennis Gulko, Davide Giraudo, Tara B, Git Gud Mar 23 '13 at 18:10

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

    
See: math.stackexchange.com/questions/112237/… –  mrf Jun 26 '12 at 15:51

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I believe there's a really nice book by Steven Krantz called Function Theory of Several Complex Variables. I know I've seen a large and organized pdf of his Complex Variables stuff, so one might think you could find the former somewhere as well...

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Though I should mention I'm not familiar with that specific textbook, only his writing style, of which I'm a fan. –  MGN Jun 26 '12 at 16:01

I have always had a soft spot for Gunning and Rossi ("Analytic Functions of Several Complex Variables"), probably because it is more "algebraic" in its approach) (sheaves, local rings, and so on. Hormander's "Introduction to Complex Analysis in Several Variables" takes what I always thought was a more "analytic" approach. I had it as a text in a course on SCV. Given your background, I might suggest Gunning-Rossi first. I have been out of touch with this area for some time. I'm sure there are more "modern" texts out there that would be fine for your purposes. Perhaps another responder could steer you toward them. I know there is a book by Stephen Krantz, for instance, but have no first-hand knowledge of it.

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