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Can anyone recommend a good comprehensive introduction to functions of several complex variables that a) is fairly up to date, b) isn't a geometry or an algebra book only, but takes multiple viewpoints? I don't mind texts that require a lot of background as long as they present it intelligibly.

Just as good would be links to lecture courses by experts on the subjects that are accessible and do the job.

I've seen Griffith/Harris, Grauert and Gunning's 3 volume treatise. Gunning looks the best of the three, but I was hoping for something more up-to-date. This is still a very active field. I haven't seen Krantz yet.

edited Jul 11 2010 at 18:02

Yemon Choi

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4 revisions, 3 users
Andrew L 67%

	I rather like Krantz's book. But I am not quite sure about the "takes multiple viewpoints" part of your requirement. – Willie Wong Jul 11 2010 at 13:12
	Well,the objects of functions of several complex variables are manifolds with a complex topological vector space structure.Therefore,they are the centerpieces of the bulk of post-19th century analysis and geometry and the tools of sheaf theory via commutative algebra are deeply interwoven in them.As a result of all this,any "pure" approach-say,emphasizing analysis-only tells part of the story. – Andrew L Jul 11 2010 at 15:49

babubba · Answer 1 · 2010-07-11 11:05:21Z UTC

I really like

Several complex variables with connections to algebraic geometry and Lie groups By Joseph L. Taylor

http://books.google.co.uk/books?id=i8lUNpZ379MC&printsec=frontcover&dq=joseph+taylor+several+complex&source=bl&ots=7MVqaXprex&sig=o63JAEz_sKc-2e63qxcSsIBYwcQ&hl=en

Anweshi · Answer 2 · 2010-07-27 20:10:47Z UTC

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For a great introduction, try Raghavan Narasimhan, "Several complex variables", Chicago lectures in mathematics.

Well-written, concise and accessible.

answered Jul 27 2010 at 20:10

Anweshi

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Functions of several complex variables: book recommendations?

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