Several Complex Variables with Connections to Algebraic Geometry and Lie Groups is popular PDF and ePub book, written by Joseph L. Taylor in 2002, it is a fantastic choice for those who relish reading online the Functions of several complex variables genre. Let's immerse ourselves in this engaging Functions of several complex variables book by exploring the summary and details provided below. Remember, Several Complex Variables with Connections to Algebraic Geometry and Lie Groups can be Read Online from any device for your convenience.
Several Complex Variables with Connections to Algebraic Geometry and Lie Groups Book PDF Summary
This text presents an integrated development of core material from several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive development of sheaf theory and the theory of coherent analytic and algebraicsheaves, proofs of the main vanishing theorems for these categories of sheaves, and a complete proof of the finite dimensionality of the cohomology of coherent sheaves on compact varieties. The vanishing theorems have a wide variety of applications and these are covered in detail. Of particular interest arethe last three chapters, which are devoted to applications of the preceding material to the study of the structure theory and representation theory of complex semisimple Lie groups. Included are introductions to harmonic analysis, the Peter-Weyl theorem, Lie theory and the structure of Lie algebras, semisimple Lie algebras and their representations, algebraic groups and the structure of complex semisimple Lie groups. All of this culminates in Milicic's proof of the Borel-Weil-Bott theorem,which makes extensive use of the material developed earlier in the text. There are numerous examples and exercises in each chapter. This modern treatment of a classic point of view would be an excellent text for a graduate course on several complex variables, as well as a useful reference for theexpert.
Detail Book of Several Complex Variables with Connections to Algebraic Geometry and Lie Groups PDF
- Author : Joseph L. Taylor
- Release : 28 June 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821831786
- Genre : Functions of several complex variables
- Total Page : 530 pages
- Language : English
- PDF File Size : 11,5 Mb
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