Several Complex Variables With Connections to Algebraic Geometry and Lie Groups

by Joseph L. Taylor

Most of the students in the graduate course from which Taylor (U. of Utah) developed this text were planning to specialize either in algebraic geometry or in the representational theory of semisimple Lie groups. He therefore simultaneously develops the fundamentals of both complex algebraic geometry and several complex variables, emphasizing the similarities in techniques of the two at the basic level. Annotation c. Book News, Inc., Portland, OR (booknews.com)

507 pages, Hardcover

First published May 14, 2002

Reviews

[Steve Dalton · Rating 4 out of 5]

This is a great book for readers who are new to algebraic/complex geometry, and would like to see both developed in parallel. I really enjoyed this book: motivation is given for every new topic introduced, and at every junction the difference between the algebraic and holomorphic cases is spelled out; often times, this leads to new excursions, because the holomorphic side is much harder to prove, or the algebraic side needs a slightly altered definition, etc.

I hesitated in giving only 4 stars, but there are numerous errors in the book (minor), and some of the later chapters don't seem to really fit the overall theme of the book (not so minor). There were also times where I was just kind of bored, though I'm not convinced that's Taylor's fault: some of this material just isn't that interesting to me.

Either way, I definitely recommend this book to anyone interested in learning some of the deep (and not-so-deep) connections between complex and algebraic geometry.