Foundations of algebraic geometry
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1962
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| Ausgabe: | Rev. and enl. ed. |
| Schriftenreihe: | Colloquium publications / American Mathematical Society
29 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Foundations of algebraic geometry |c by André Weil |
| 250 | |a Rev. and enl. ed. | ||
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1962 | |
| 300 | |a XX, 363 S. | ||
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| 490 | 1 | |a Colloquium publications / American Mathematical Society |v 29 | |
| 650 | 4 | |a Geometry, Algebraic | |
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Datensatz im Suchindex
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| adam_text | TABLE OF CONTENTS
PAGE
Introduction
Introduction (1944) vii
Advice to the reader xiii
Table of notations xvii
Chapter I. Algebraic preliminaries
§1. Notations 1
§2. Dimension; independence; linear disjointness 2
§3. Ideal determined by a set of quantities over a field 6
§4. Separability; sets of conjugates 8
§5. Derivations 11
§6. Extending the field of reference 14
§7. Regular extensions 16
§8. The order of inseparability 21
Chapter II. Algebraic theory of specializations
§1. Specializations 26
§2. Extension of specializations 30
§3. Applications 32
§4. Specialization rings 36
§5. Finiteness over a specialization 41
§6. Generalizations 43
Chapter III. Analytic theory of specializations
§1. Ideals in arbitrary rings 45
§2. Ideals in polynomial rings 48
§3. Rings of power series 50
§4. The multiplicity of a specialization 61
Chapter IV. The geometric language
§1. Points and varieties 68
§2. Isomorphisms; conjugate varieties; specialization rings 75
§3. Product varieties and projections 78
§4. Unions and intersections of varieties 84
§5. Linear varieties 90
§6. Simple points 97
§7. Projection from a variety and birational correspondences 105
Chapter V. Intersection multiplicities (special case)
§1. Intersections of dimension 0 116
§2. Intersections of arbitrary dimension 129
§3. The theory of simple points 135
Chapter VI. General intersection theory
§1. Definition of the symbol i(AB, C; U) 142
§2. Properties of the symbol i(A B, C; U) 149
§3. Intersections in product varieties 153
v
vi CONTENTS
PAGE
Chapter VII. The geometry on abstract varieties
§1. The Zariski topology 166
§2. Mappings and morphisms 170
§3. Abstract varieties 179
§4. The topology of abstract varieties 185
§5. Products and projections 189
§6. Mappings of abstract varieties 195
§7. Intersection multiplicities 200
Chapter VIII. The calculus op cycles
§1. Chains and cycles 206
§2. Chains and cycles of dimension 0 213
§3. Fundamental operations on chains and cycles 219
§4. Images and counterimages of cycles 231
Chapter IX. Divisors and linear systems
§1. Mappings into curves 243
§2. Divisors of functions 245
§3. Some auxiliary results 255
§4. Qualitative theory of divisors 261
§5. Linear systems and projective spaces 269
§6. The generic divisors of a linear system 293
Chapter X. Comments and discussions
§1. Qualitative and quantitative algebraic geometry 304
§2. The universal domain 305
§3. The concept of affine variety 308
§4. Derivations and differential forms 309
§5. Specializations : 311
§6. The theory of intersections 316
§7. Abstract varieties and their generalizations 320
§8. Comments on Chapter IX 325
§9. Equivalence theories and open questions 328
Appendix I. Normal varieties and normalization 334
Appendix II. Characterization or the i symbol by its properties 349
Appendix III. Varieties over topological fields 352
Indf.x of Definitions 359
|
| any_adam_object | 1 |
| author | Weil, André 1906-1998 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Rev. and enl. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-25T17:10:36Z |
| institution | BVB |
| language | English |
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| physical | XX, 363 S. |
| publishDate | 1962 |
| publishDateSearch | 1962 |
| publishDateSort | 1962 |
| publisher | American Math. Soc. |
| record_format | marc |
| series2 | Colloquium publications / American Mathematical Society |
| spellingShingle | Weil, André 1906-1998 Foundations of algebraic geometry Geometry, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4001161-6 |
| title | Foundations of algebraic geometry |
| title_auth | Foundations of algebraic geometry |
| title_exact_search | Foundations of algebraic geometry |
| title_full | Foundations of algebraic geometry by André Weil |
| title_fullStr | Foundations of algebraic geometry by André Weil |
| title_full_unstemmed | Foundations of algebraic geometry by André Weil |
| title_short | Foundations of algebraic geometry |
| title_sort | foundations of algebraic geometry |
| topic | Geometry, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Geometry, Algebraic Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002331885&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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