عنوان

Several complex variables with connections to algebraic geometry and Lie groups /

شابک

082183178X

شابک

9780821831786

شماره

dltt

عنوان اصلي

Several complex variables with connections to algebraic geometry and Lie groups /

نام عام مواد

[Book]

نام نخستين پديدآور

Joseph L. Taylor

نام خاص و کميت اثر

xvi, 507 pages ;

ابعاد

26 cm

عنوان فروست

Graduate studies in mathematics,

مشخصه جلد

v. 46

شاپا ي ISSN فروست

1065-7339 ;

متن يادداشت

Includes bibliographical references (pages 497-499) and index

متن يادداشت

Ch. 1. Selected Problems in One Complex Variable -- 1.1. Preliminaries -- 1.2. A Simple Problem -- 1.3. Partitions of Unity -- 1.4. The Cauchy-Riemann Equations -- 1.5. The Proof of Proposition 1.2.2 -- 1.6. The Mittag-Leffler and Weierstrass Theorems -- 1.7. Conclusions and Comments -- Ch. 2. Holomorphic Functions of Several Variables -- 2.1. Cauchy's Formula and Power Series Expansions -- 2.2. Hartog's Theorem -- 2.3. The Cauchy-Riemann Equations -- 2.4. Convergence Theorems -- 2.5. Domains of Holomorphy -- Ch. 3. Local Rings and Varieties -- 3.1. Rings of Germs of Holomorphic Functions -- 3.2. Hilbert's Basis Theorem -- 3.3. The Weierstrass Theorems -- 3.4. The Local Ring of Holomorphic Functions is Noetherian -- 3.5. Varieties -- 3.6. Irreducible Varieties -- 3.7. Implicit and Inverse Mapping Theorems -- 3.8. Holomorphic Functions on a Subvariety -- Ch. 4. The Nullstellensatz -- 4.1. Reduction to the Case of Prime Ideals -- 4.2. Survey of Results on Ring and Field Extensions -- 4.3. Hilbert's Nullstellensatz -- 4.4. Finite Branched Holomorphic Covers -- 4.5. The Nullstellensatz -- 4.6. Morphisms of Germs of Varieties -- Ch. 5. Dimension -- 5.1. Topological Dimension -- 5.2. Subvarieties of Codimension 1 -- 5.3. Krull Dimension -- 5.4. Tangential Dimension -- 5.5. Dimension and Regularity -- 5.6. Dimension of Algebraic Varieties -- 5.7. Algebraic vs. Holomorphic Dimension -- Ch. 6. Homological Algebra -- 6.1. Abelian Categories -- 6.2. Complexes -- 6.3. Injective and Projective Resolutions -- 6.4. Higher Derived Functors -- 6.5. Ext -- 6.6. The Category of Modules, Tor -- 6.7. Hilbert's Syzygy Theorem -- Ch. 7. Sheaves and Sheaf Cohomology -- 7.1. Sheaves -- 7.2. Morphisms of Sheaves -- 7.3. Operations on Sheaves -- 7.4. Sheaf Cohomology -- 7.5. Classes of Acyclic Sheaves -- 7.6. Ringed Spaces -- 7.7. De Rham Cohomology -- 7.8. Cech Cohomology -- 7.9. Line Bundles and Cech Cohomology -- Ch. 8. Coherent Algebraic Sheaves -- 8.1. Abstract Varieties -- 8.2. Localization -- 8.3. Coherent and Quasi-coherent Algebraic Sheaves -- 8.4. Theorems of Artin-Rees and Krull -- 8.5. The Vanishing Theorem for Quasi-coherent Sheaves -- 8.6. Cohomological Characterization of Affine Varieties -- 8.7. Morphisms -- Direct and Inverse Image -- 8.8. An Open Mapping Theorem -- Ch. 9. Coherent Analytic Sheaves -- 9.1. Coherence in the Analytic Case -- 9.2. Oka's Theorem -- 9.3. Ideal Sheaves -- 9.4. Coherent Sheaves on Varieties -- 9.5. Morphisms between Coherent Sheaves -- 9.6. Direct and Inverse Image -- Ch. 10. Stein Spaces -- 10.1. Dolbeault Cohomology -- 10.2. Chains of Syzygies -- 10.3. Functional Analysis Preliminaries -- 10.4. Cartan's Factorization Lemma -- 10.5. Amalgamation of Syzygies -- 10.6. Stein Spaces -- Ch. 11. Frechet Sheaves -- Cartan's Theorems -- 11.1. Topological Vector Spaces -- 11.2. The Topology of H(X) -- 11.3. Frechet Sheaves -- 11.4. Cartan's Theorems -- 11.5. Applications of Cartan's Theorems -- 11.6. Invertible Groups and Line Bundles -- 11.7. Meromorphic Functions -- 11.8. Holomorphic Functional Calculus -- 11.9. Localization -- 11.10. Coherent Sheaves on Compact Varieties -- 11.11. Schwartz's Theorem -- Ch. 12. Projective Varieties -- 12.1. Complex Projective Space -- 12.2. Projective Space as an Algebraic and a Holomorphic Variety -- 12.3. The Sheaves O(k) and H(k) -- 12.4. Applications of the Sheaves O(k) -- 12.5. Embeddings in Projective Space -- Ch. 13. Algebraic vs. Analytic -- Serre's Theorems -- 13.1. Faithfully Flat Ring Extensions -- 13.2. Completion of Local Rings -- 13.3. Local Rings of Algebraic vs. Holomorphic Functions -- 13.4. The Algebraic to Holomorphic Functor -- 13.5. Serre's Theorems -- 13.6. Applications -- Ch. 14. Lie Groups and Their Representations -- 14.1. Topological Groups -- 14.2. Compact Topological Groups -- 14.3. Lie Groups and Lie Algebras -- 14.4. Lie Algebras -- 14.5. Structure of Semisimple Lie Algebras -- 14.6. Representations of [actual symbol not reproducible][subscript 2]([Complex number system]) -- 14.7. Representations of Semisimple Lie Algebras -- 14.8. Compact Semisimple Groups -- Ch. 15. Algebraic Groups -- 15.1. Algebraic Groups and Their Representations -- 15.2. Quotients and Group Actions -- 15.3. Existence of the Quotient -- 15.4. Jordan Decomposition -- 15.5. Tori -- 15.6. Solvable Algebraic Groups -- 15.7. Semisimple Groups and Borel Subgroups -- 15.8. Complex Semisimple Lie Groups -- Ch. 16. The Borel-Weil-Bott Theorem -- 16.1. Vector Bundles and Induced Representations -- 16.2. Equivariant Line Bundles on the Flag Variety -- 16.3. The Casimir Operator -- 16.4. The Borel-Weil Theorem -- 16.5. The Borel-Weil-Bott Theorem -- 16.6. Consequences for Real Semisimple Lie Groups -- 16.7. Infinite Dimensional Representations

بدون عنوان

0

موضوع مستند نشده

Functions of several complex variables

موضوع مستند نشده

Geometry, Algebraic

موضوع مستند نشده

Algebraïsche meetkunde

موضوع مستند نشده

Complexe variabelen

موضوع مستند نشده

GEOMETRIA ALGÉBRICA

موضوع مستند نشده

Lie-groepen

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Taylor, Joseph L.,1941-

تاريخ عمليات

20160712071453.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y