[Math] Functions of several complex variables: book recommendations

cv.complex-variablesseveral-complex-variablestextbook-recommendation

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.

Best Answer

I know this is somewhat late answer for the original question, but here goes. I've taught Several Complex Variables twice at Oklahoma State, and I wrote a hopefully easy to read textbook for the purpose. It is freely available online under a CC license:

http://www.jirka.org/scv/

It is not a reference work, it is a hopefully gentle introduction, something that would be covered in one semester by a beginning graduate student after at least one semester of one complex variable. It doesn't cover anything too deeply, but I did try to cover several different viewpoints rather than focus on one specific thing.

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