Introduction to complex analytic geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Polish |
| Published: |
Basel u.a.
Birkhäuser
1991
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Poln. übers. |
| Physical Description: | XIV, 523 S. |
| ISBN: | 3764319356 0817619356 |
Staff View
MARC
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| 240 | 1 | 0 | |a Wstȩp do geometrii analitycznej zespolonej |
| 245 | 1 | 0 | |a Introduction to complex analytic geometry |c Stanisław Łojasiewicz |
| 264 | 1 | |a Basel u.a. |b Birkhäuser |c 1991 | |
| 300 | |a XIV, 523 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Aus d. Poln. übers. | ||
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| 650 | 7 | |a Fonctions d'une variable complexe |2 ram | |
| 650 | 7 | |a Géométrie analytique |2 ram | |
| 650 | 4 | |a Analytic spaces | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 4 | |a Geometry, Analytic | |
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Record in the Search Index
| _version_ | 1804118684660137984 |
|---|---|
| adam_text | CONTENTS
Preface to the Polish Edition v
Preface to the English Edition ix
PRELIMINARIES
CHAPTER A. Algebra 1
§ 1. Rings, fields, modules, ideals, vector spaces 1
§ 2. Polynomials 15
§ 3. Polynomial mappings 20
§ 4. Symmetric polynomials. Discriminant 23
§ 5. Extensions of fields 26
§ 6. Factorial rings 27
§ 7. Primitive element theorem 29
§ 8. Extensions of rings 30
§ 9. Noetherian rings 34
§10. Local rings 39
§11. Localization 46
§12. Krull s dimension 53
§13. Modules of syzygies and homological dimension 57
§14. The depth of a module 61
§15. Regular rings 66
CHAPTER B. Topology 72
§ 1. Some topological properties of sets and families of sets 72
§ 2. Open, closed and proper mappings 74
§ 3. Local homeomorphisms and coverings 77
§ 4. Germs of sets and functions 80
§ 5. The topology of a finite dimensional vector space
(over C or R) 84
§ 6. The topology of the Grassmann space 87
xii Contents
CHAPTER C. Complex analysis 98
§ 1. Holomorphic mappings 98
§ 2. The Weierstrass preparation theorem 109
§ 3. Complex manifolds 112
§ 4. The rank theorem. Submersions 134
COMPLEX ANALYTIC GEOMETRY
CHAPTER I. Rings of germs of holomorphic functions 139
§ 1. Elementary properties. Noether and local properties.
Regularity 139
§ 2. Unique factorization property 145
§ 3. The Preparation Theorem in Thom Martinet version 147
CHAPTER II. Analytic sets, analytic germs and their ideals 150
§ 1. Dimension 150
§ 2. Thin sets 152
§ 3. Analytic sets and germs 153
§ 4. Ideals of germs and the loci of ideals. Decomposition into
simple germs 160
§ 5. Principal germs 164
§ 6. One dimensional germs. The Puiseux theorem 170
CHAPTER III. Fundamental lemmas 178
§ 1. Lemmas on quasi covers 178
§ 2. Regular and k normal ideals and germs 183
§ 3. Riickert s descriptive lemma 188
§ 4. Hilbert s Nullstellensatz and other consequences
(concerning dimension, regularity and fc normality) 196
CHAPTER IV. Geometry of analytic sets 203
§ 1. Normal triples 203
§ 2. Regular and singular points. Decomposition into simple
components 208
Contents xiii
§ 3. Some properties of analytic germs and sets 221
§ 4. The ring of an analytic germ. Zariski s dimension 225
§ 5. The maximum principle 234
§ 6. The Remmert Stein removable singularity theorem 237
§ 7. Regular separation 242
§ 8. Analytically constructible sets 245
CHAPTER V. Holomorphic mappings 254
§ 1. Some properties of holomorphic mappings of manifolds 254
§ 2. The multiplicity theorem. Rouche s theorem 256
§ 3. Holomorphic mappings of analytic sets 264
§ 4. Analytic spaces 275
§ 5. Remmert s proper mapping theorem 289
§ 6. Remmert s open mapping theorem 294
§ 7. Finite holomorphic mappings 299
§ 8. c holomorphic mappings 311
CHAPTER VI. Normalization 314
§ 1. The Cartan and Oka coherence theorems 314
§ 2. Normal spaces. Universal denominators 332
§ 3. Normal points of analytic spaces 337
§ 4. Normalization 343
CHAPTER VII. Analyticity and algebraicity 352
§ 1. Algebraic sets and their ideals 352
§ 2. The projective space as a manifold 355
§ 3. The projective closure of a vector space 359
§ 4. Grassmann manifolds 364
§ 5. Blowings up 371
§ 6. Algebraic sets in projective spaces. Chow s theorem 381
§ 7. The Rudin and Sadullaev theorems 388
§ 8. Constructible sets. The Chevalley theorem 392
§ 9. Riickert s lemma for algebraic sets 400
§10. Hilbert s Nullstellensatz for polynomials 404
§11. Further properties of algebraic sets.
Principal varieties. Degree 407
§12. The ring of an algebraic subset of a vector space 425
xiv Contents
§13. Bezout s theorem. Biholomorphic mappings
of projective spaces 430
§14. Meromorphic functions and rational functions 438
§15. Ideals of On with polynomial generators 456
§16. Serre s algebraic graph theorem. 459
§17. Algebraic spaces 472
§18. Biholomorphic mappings of factorial subsets
in projective spaces 487
§19. The Andreotti Salmon theorem 492
§20. Chow s theorem on biholomorphic mappings
of Grassmann manifolds 502
References 507
Notation index 511
Subject index 514
|
| any_adam_object | 1 |
| author | Łojasiewicz, Stanisław 1926-2002 |
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| author_variant | s ł sł |
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| 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.BV004552838 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:14:13Z |
| institution | BVB |
| isbn | 3764319356 0817619356 |
| language | English Polish |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002801884 |
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| physical | XIV, 523 S. |
| publishDate | 1991 |
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| publisher | Birkhäuser |
| record_format | marc |
| spelling | Łojasiewicz, Stanisław 1926-2002 Verfasser (DE-588)133630595 aut Wstȩp do geometrii analitycznej zespolonej Introduction to complex analytic geometry Stanisław Łojasiewicz Basel u.a. Birkhäuser 1991 XIV, 523 S. txt rdacontent n rdamedia nc rdacarrier Aus d. Poln. übers. Espaces analytiques ram Fonctions d'une variable complexe ram Géométrie analytique ram Analytic spaces Functions of complex variables Geometry, Analytic Komplexe analytische Geometrie (DE-588)4280577-6 gnd rswk-swf Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Komplexe analytische Geometrie (DE-588)4280577-6 s DE-604 Analytische Geometrie (DE-588)4001867-2 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002801884&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Łojasiewicz, Stanisław 1926-2002 Introduction to complex analytic geometry Espaces analytiques ram Fonctions d'une variable complexe ram Géométrie analytique ram Analytic spaces Functions of complex variables Geometry, Analytic Komplexe analytische Geometrie (DE-588)4280577-6 gnd Analytische Geometrie (DE-588)4001867-2 gnd |
| subject_GND | (DE-588)4280577-6 (DE-588)4001867-2 |
| title | Introduction to complex analytic geometry |
| title_alt | Wstȩp do geometrii analitycznej zespolonej |
| title_auth | Introduction to complex analytic geometry |
| title_exact_search | Introduction to complex analytic geometry |
| title_full | Introduction to complex analytic geometry Stanisław Łojasiewicz |
| title_fullStr | Introduction to complex analytic geometry Stanisław Łojasiewicz |
| title_full_unstemmed | Introduction to complex analytic geometry Stanisław Łojasiewicz |
| title_short | Introduction to complex analytic geometry |
| title_sort | introduction to complex analytic geometry |
| topic | Espaces analytiques ram Fonctions d'une variable complexe ram Géométrie analytique ram Analytic spaces Functions of complex variables Geometry, Analytic Komplexe analytische Geometrie (DE-588)4280577-6 gnd Analytische Geometrie (DE-588)4001867-2 gnd |
| topic_facet | Espaces analytiques Fonctions d'une variable complexe Géométrie analytique Analytic spaces Functions of complex variables Geometry, Analytic Komplexe analytische Geometrie Analytische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002801884&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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