Complex analytic varieties:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Addison-Wesley Publishing Company
1972
|
| Schriftenreihe: | Addison-Wesley Series in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 399 Seiten |
Internformat
MARC
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| 100 | 1 | |a Whitney, Hassler |d 1907-1989 |e Verfasser |0 (DE-588)11904045X |4 aut | |
| 245 | 1 | 0 | |a Complex analytic varieties |c Hassler Whitney, The Institute for Advanced Study, Princeton, New Jersey |
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley Publishing Company |c 1972 | |
| 300 | |a XII, 399 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Addison-Wesley Series in Mathematics | |
| 650 | 4 | |a Espaces analytiques | |
| 650 | 4 | |a Fonctions analytiques | |
| 650 | 7 | |a Fonctions d'une variable complexe |2 ram | |
| 650 | 4 | |a Analytic functions | |
| 650 | 4 | |a Analytic spaces | |
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Datensatz im Suchindex
| _version_ | 1804118284305432576 |
|---|---|
| adam_text | CONTENTS
Chapter 1 Holomorphic Functions in C
1. Complex n space C 1
2. Planes, projections, polydisks 3
3. Holomorphic functions in C 7
4. Order of vanishing 11
5. The Weierstrass preparation and division theorems 14
6. Thin sets 19
7. Holomorphic multifunctions 20
8. Properties of holomorphic multifunctions 23
9. Factoring, divisibility 26
10. Fractional power series 31
11. Germs of functions 32
12. Some basic properties of O 34
13. A certain ring of holomorphic functions 37
Chapter 2 Analytic Varieties
1. Elementary properties of varieties 41
2. Simple points 44
3. Cartesian products, holomorphic mappings 45
4. Elimination, projections 47
5. The Hartogs extension theorem 50
6. W type varieties 51
7. Local W type varieties for V 53
8. Some simple examples 55
9. Dimension 61
10. Hypervarieties 64
11. Further properties of dimension 67
12. Products, intersections, sections 70
Chapter 3 General Properties of Varieties
1. Irreducible varieties 73
2. Irreducible components 77
3. The representation theorem 80
4. Further theorems about representation 83
5. Analyticity of closures of varieties 87
6. The singular variety of a variety 89
ix
x Contents
7. Tangent vector fields 94
8. Germs of varieties 96
9. Intersections of germs and varieties 100
Chapter 4 Holomorphic and Weakly Holomorphic Functions
1. Holomorphic functions and mappings 103
2. Continuous weakly holomorphic functions 107
3. Weakly holomorphic functions . 110
4. Universal denominators 114
5. c Holomorphic mappings 118
6. Fibers of c holomorphic mappings 121
7. The rank of a mapping 125
8. Rank over subvarieties 127
9. Germs of functions on a variety 130
10. Germs of weakly holomorphic functions . 132
11. Local biholomorphisms 135
Chapter 5 Analytic Spaces
1. Definitions 140
2. Alternative definition, construction 143
3. Elementary properties of analytic spaces 146
4. The proper mapping theorem 150
5. The analytic space of symmetric powers 152
6. Minimal coordinate systems 154
Derivations 157
8. Complex projective spaces 162
9. Projective varieties 164
10. Multiprojective spaces 166
11. Multiprojective varieties 168
12. Some properties of projective varieties 171
13. Complex Grassmann spaces 175
14. Metrics in P 1 and in G m 178
Chapter 6 Meromorphic Mappings, Modifications, Dependence
1. Meromorphic functions 183
2. Modifications 187
3. Meromorphic mappings 190
4. General properties 194
5. Analytic dependence 197
6. Algebraic dependence 200
7. Fields of meromorphic functions 203
8. Algebraic closures 205
Chapter 7 Tangents
1. Possible definitions of tangents 209
2. Tangent cones 212
Contents xi
3. Tangents and differentiable curves 215
4. Algebraic expression for tangent cones 219
5. Intrinsic definition of tangent cones 223
6. Tangent cones and mappings 228
7. Multiplicity in a variety 232
8. Multiplicity varieties 236
9. Coverings, dimension of fibers 239
10. Good planes 241
11. Semiproper mappings 245
Chapter 8 Normalization
1. Normal points 250
2. Local normalization 253
3. Normalization 256
4. Tangents relative to a subvariety 259
5. Certain nonnormal points 263
6. Some particular universal denominators 268
7. Presheaves 271
8. Presheaves of relations 275
9. The ideal presheaf of a variety 280
10. The set of normal points is open 283
Appendix I Topological Preliminaries
1. Topological spaces 286
2. Metric spaces 288
3. Functions 289
4. Proper mappings 292
Appendix II Smooth Mappings, Manifolds
1. Smooth mappings 294
2. Regular and open mappings 298
3. Inverse and implicit functions 301
4. Coordinate systems, manifolds in A11 304
5. Tangents; mappings of manifolds 307
6. Functions vanishing on a manifold 310
7. Mappings of constant rank 312
Appendix III Functions of a Complex Variable
1. Complex numbers and functions 316
2. Line integrals 317
3. Removable singularities 319
4. Power series 320
5. Zeros and poles 320
6. Local mappings 323
7. Rado s theorem 324
8. Interpolation 326
xii Contents
Appendix IV Algebraic Methods
1. Integral domains 330
2. Unique factorization domains 331
3. Polynomials 332
4. Polynomials in several variables 335
5. Homogeneous polynomials; order 336
6. Factoring polynomials 337
7. Linear equations 340
8. The resultant of two polynomials 341
9. The resultant in terms of roots 344
10. The discriminant of a polynomial 345
11. Multiple roots 348
12. Ideals 350
Appendix V Symmetric Powers
1. Summary 354
2. Symmetric powers 359
3. Topology in X^ 361
4. Continuity of roots 363
5. Imbedding (KTsym in K 365
6. Properties of fi and (j) 367
7. Canonical equations for a 369
8. Sums; number of distinct elements 370
9. Multifunctions 372
10. Splitting multifunctions 375
Bibliography 380
Index of Notations 387
Index 393
|
| any_adam_object | 1 |
| author | Whitney, Hassler 1907-1989 |
| author_GND | (DE-588)11904045X |
| author_facet | Whitney, Hassler 1907-1989 |
| author_role | aut |
| author_sort | Whitney, Hassler 1907-1989 |
| author_variant | h w hw |
| building | Verbundindex |
| bvnumber | BV004053407 |
| callnumber-first | Q - Science |
| callnumber-label | QA331 |
| callnumber-raw | QA331 |
| callnumber-search | QA331 |
| callnumber-sort | QA 3331 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 780 SK 370 |
| ctrlnum | (OCoLC)539495 (DE-599)BVBBV004053407 |
| dewey-full | 515/.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.9 |
| dewey-search | 515/.9 |
| dewey-sort | 3515 19 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004053407 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:07:51Z |
| institution | BVB |
| language | English |
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| physical | XII, 399 Seiten |
| psigel | TUB-www |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Addison-Wesley Publishing Company |
| record_format | marc |
| series2 | Addison-Wesley Series in Mathematics |
| spelling | Whitney, Hassler 1907-1989 Verfasser (DE-588)11904045X aut Complex analytic varieties Hassler Whitney, The Institute for Advanced Study, Princeton, New Jersey Reading, Mass. [u.a.] Addison-Wesley Publishing Company 1972 XII, 399 Seiten txt rdacontent n rdamedia nc rdacarrier Addison-Wesley Series in Mathematics Espaces analytiques Fonctions analytiques Fonctions d'une variable complexe ram Analytic functions Analytic spaces Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 s DE-604 Analytische Funktion (DE-588)4142348-3 s Komplexe Variable (DE-588)4164905-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002534979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Whitney, Hassler 1907-1989 Complex analytic varieties Espaces analytiques Fonctions analytiques Fonctions d'une variable complexe ram Analytic functions Analytic spaces Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Analytische Funktion (DE-588)4142348-3 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| subject_GND | (DE-588)4031996-9 (DE-588)4142348-3 (DE-588)4164905-9 |
| title | Complex analytic varieties |
| title_auth | Complex analytic varieties |
| title_exact_search | Complex analytic varieties |
| title_full | Complex analytic varieties Hassler Whitney, The Institute for Advanced Study, Princeton, New Jersey |
| title_fullStr | Complex analytic varieties Hassler Whitney, The Institute for Advanced Study, Princeton, New Jersey |
| title_full_unstemmed | Complex analytic varieties Hassler Whitney, The Institute for Advanced Study, Princeton, New Jersey |
| title_short | Complex analytic varieties |
| title_sort | complex analytic varieties |
| topic | Espaces analytiques Fonctions analytiques Fonctions d'une variable complexe ram Analytic functions Analytic spaces Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Analytische Funktion (DE-588)4142348-3 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| topic_facet | Espaces analytiques Fonctions analytiques Fonctions d'une variable complexe Analytic functions Analytic spaces Komplexe Mannigfaltigkeit Analytische Funktion Komplexe Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002534979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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