Several Complex Variables with Connections to Algebraic Geometry and Lie Groups (Graduate Studies in Mathematics, V. 46)

Taylor, Joseph

ISBN 10: 082183178X / ISBN 13: 9780821831786

Edité par Amer Mathematical Society, 2002

A propos de cet article

Presents an integrated development of the theory of 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. This text includes a treatment of the local theory. Series: Graduate Studies in Mathematics. Num Pages: 528 pages, bibliography, index. BIC Classification: PBKF; PBMW; PBPD. Category: (P) Professional & Vocational. Dimension: 230. Weight in Grams: 1128. . 2002. Hardcover. . . . . Books ship from the US and Ireland.

N° de réf. du vendeur V9780821831786

Détails bibliographiques

• Titre: Several Complex Variables with Connections to Algebraic Geometry and Lie Groups (Graduate Studies in Mathematics, V. 46)
• Éditeur: Amer Mathematical Society
• Date de parution: 2002
• Langue: anglais
• ISBN à 10 chiffres: 082183178X
• ISBN à 13 chiffres: 9780821831786
• Reliure: Couverture rigide
• État de l'article: New

A propos de ce titre

Synopsis

This text presents an integrated development of the theory of 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 algebraic sheaves, 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 are the last three chapters, which are devoted to applications of the preceding material to the study of the structure and representations of complex semisimple Lie groups.Included in this text 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 the expert.