A primer of algebraic geometry: constructive computational methods
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
2000
|
| Series: | Pure and applied mathematics
227 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 370 S. |
| ISBN: | 082470374X |
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MARC
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| 245 | 1 | 0 | |a A primer of algebraic geometry |b constructive computational methods |c Huishi Li ; Freddy Van Oystaeyen |
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Record in the Search Index
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| adam_text | Contents
PREFACE iii
NOTATION xiii
CHAPTER I. Affine Algebraic Sets and the
Nullstellensatz l
§1. Polynomials and Affine Space 1
§2. Affine Algebraic Sets 9
§3. Parametrizations of Algebraic Sets 11
§4. Ideals for Algebraic Sets 21
§5. Hilbert s Nullstellensatz 22
§6. Radical Ideals and the Nullstellensatz 27
CHAPTER II. Polynomial and Rational
Functions 33
§1. The Zariski Topology and Irreducible Algebraic Sets 34
§2. Decomposition of an Algebraic Set 40
§3. Polynomial Mappings and Polynomial Functions 43
§4. The Coordinate Ring of an Algebraic Set 48
§5. Affine Change of Coordinates 56
§6. Rational Functions and Local Rings 58
ix
x Contents
CHAPTER III. Projective Algebraic Sets 69
§1. Projective Space 71
§2. The Projective Algebra Geometry Dictionary 78
§3. Homogeneous Coordinate Ring and Function Field 82
§4. Projective Change of Coordinates 85
§5. Dehomogenization and Homogenization of Polynomials 90
§6. Amne Projective Transfer of Algebraic Sets 95
§7. Multiprojective Space and Segre Product 106
CHAPTER IV. Groebner Basis ill
§1. Monomial Order ings 111
§2. A Division Algorithm in k[xi, ...,xn] 120
§3. Monomial Ideals and Dickson s Lemma 128
§4. Hilbert Basis Theorem and Groebner Basis 133
§5. Applications to Previous Chapters 139
CHAPTER V. Dimension of Algebraic Sets 147
§1. The Algebraic Set of a Monomial Ideal 150
§2. The Vector Space k[xi,...,xn]/I 155
§3. Hilbert Function and dimV 159
§4. The Dimension of a Projective Algebraic Set 173
§5. Elementary Properties of Dimension 179
§6. Dimension and Algebraic Independence 186
§7. Dimension and Elimination of Variables 192
§8. The Krull Dimension of an Affine fc Algebra 200
§9. The Topological Dimension of an Affine Algebraic Set 205
CHAPTER VI. An Introduction to Local
Theory 207
§1. Regular Functions on Quasi Varieties 209
§2. Morphisms 215
§3. Rational Maps 225
§4. Examples of Rational Varieties 233
§5. An Algorithm Checking the Birationality of Rational
Maps 238
§6. Nonsingular Points in Algebraic Sets 240
Contents xi
CHAPTER VII. Curves 253
§1. Nonsingular Curves 253
§2. Intersection of Curves 265
§3. Bezout s Theorem 277
§4. Divisors on Curves 283
§5. The Linear Space C{D) 290
§6. The Riemann Roch Theorem 297
CHAPTER VIII. Elliptic Curves 307
§1. Standard Equation for Nonsingular Cubic Curve 308
§2. Addition on an Elliptic Curve 315
§3. Elliptic Functions and Weierstrass Theory 327
APPENDIX I. Finiteness Conditions and Field
Extensions 343
§1. Modules, Finiteness Conditions 343
§2. Integral Elements 346
§3. Ring finite Field Extensions 348
§4. Existence of a Primitive Element 350
APPENDIX II. Localization, Discrete Valuation
Rings and Dedekind Domains 355
§1. Localization at a Multiplicative Subset 355
§2. Discrete Valuation Rings 357
§3. Dedekind Domains 361
REFERENCES 365
INDEX 367
|
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| id | DE-604.BV013050835 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:38:18Z |
| institution | BVB |
| isbn | 082470374X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008892663 |
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| physical | XIII, 370 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Li, Huishi 1955- Verfasser (DE-588)123969034 aut A primer of algebraic geometry constructive computational methods Huishi Li ; Freddy Van Oystaeyen New York [u.a.] Dekker 2000 XIII, 370 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 227 Géométrie algébrique ram Geometry, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s DE-604 Van Oystaeyen, Freddy 1947- Verfasser (DE-588)128792884 aut Pure and applied mathematics 227 (DE-604)BV000001885 227 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008892663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Li, Huishi 1955- Van Oystaeyen, Freddy 1947- A primer of algebraic geometry constructive computational methods Pure and applied mathematics Géométrie algébrique ram Geometry, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4001161-6 |
| title | A primer of algebraic geometry constructive computational methods |
| title_auth | A primer of algebraic geometry constructive computational methods |
| title_exact_search | A primer of algebraic geometry constructive computational methods |
| title_full | A primer of algebraic geometry constructive computational methods Huishi Li ; Freddy Van Oystaeyen |
| title_fullStr | A primer of algebraic geometry constructive computational methods Huishi Li ; Freddy Van Oystaeyen |
| title_full_unstemmed | A primer of algebraic geometry constructive computational methods Huishi Li ; Freddy Van Oystaeyen |
| title_short | A primer of algebraic geometry |
| title_sort | a primer of algebraic geometry constructive computational methods |
| title_sub | constructive computational methods |
| topic | Géométrie algébrique ram Geometry, Algebraic Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Géométrie algébrique Geometry, Algebraic Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008892663&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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