Tasty Bits of Several Complex Variables

A whirlwind tour of the subject

By: Jiří Lebl (website #1 http://www.jirka.org/ (personal), website #2 http://www.math.okstate.edu/~lebl/ (work: OSU), email: )

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This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semesters at Oklahoma State University. It should be suitable for a semester-long topics course or for self-study as an introduction to the subject.

The prerequisites are decent knowledge of vector calculus, basic real-analysis and a working knowledge of complex analysis in one variable. It should be accessible to beginning graduate students after a complex analysis course, and perhaps even very advanced undergraduates.

Overall it should be enough material for a semester-long course, though that of course depends on the speed of the lecturer. There are quite a few exercises sprinkled throughout the text, and I am assuming that a reader is at least attempting all of them.

This book is not meant as an exhaustive reference. It is simply a whirlwind tour of several complex variables. To find the list of the books useful for reference and further reading, see the end of the book.

Do let me know if there are typos or errors. You can email me at .

This book may be modified and customized for a specific purpose if necessary. If you do modify the book, make sure to mark it prominently as such to avoid confusion. This aspect is also important for longevity of the book. The book can be updated and modified even if I happen to drop off the face of the earth. You do not have to depend on any publisher being interested as with traditional textbooks.

Table of contents:

1. Holomorphic functions in several variables
2. Convexity and pseudoconvexity
3. CR Geometry
4. The dbar-problem
5. Integral kernels
6. Complex analytic varieties

There are 217 exercises in the book of various difficulty.


Download the book as PDF
(Version 2.2, November 29th, 2017, 140 pages)

See the errata in the current version.

Look at the change log to see what changed in the newest version (You can download source files of old versions if you wish).

Buy paperback:

Buy a copy at lulu.com for $8.10 (the discounted price on lulu). I get approx $2, so by buying a copy you will support this project. You will also save your toner cartridge. The ISBN is 978-1-365-09557-3 and you can also buy it on Amazon, Barns and Noble, and Ingram, although these are a bit more expensive ($13.50) and it always takes a few weeks before a new update appears.

You can also buy a larger (letter size) coil-bound copy at lulu.com for $11.50.


The source is now hosted on GitHub: https://github.com/jirilebl/scv

You can get an archive of the source of the released version on github, look under https://github.com/jirilebl/scv/releases, though if you plan to work with it, maybe best to look at just the latest working version as that might have any errata or new additions. Though these might be a work in progress. Perhaps best is to let me know.

The main file is scv.tex. I compile the pdf with pdflatex. You also want to run makeindex to generate the index (I generally run pdflatex scv three times, then makeindex scv, and then finally pdflatex scv again)..

The github 'master' version is the current working version, so it will have whatever new changes I make in my tree.


Creative Commons License Creative Commons License This work is dual licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License and Creative Commons Attribution-Share Alike 4.0 License. You can use, print, copy, and share this book as much as you want. You can base your own book/notes on these and reuse parts if you keep the license the same (that is, as long as you use at least one of the two licenses).

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