An invitation to algebraic geometry:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 161 S. Ill., graph. Darst. |
| ISBN: | 0387989803 |
Staff View
MARC
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| 245 | 1 | 0 | |a An invitation to algebraic geometry |c Karen E. Smith ... |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2000 | |
| 300 | |a XVI, 161 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 4 | |a Geometría algebraica | |
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| 689 | 0 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
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| 700 | 1 | |a Smith, Karen E. |d 1965- |e Sonstige |0 (DE-588)128408677 |4 oth | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009057227 | ||
Record in the Search Index
| _version_ | 1804128052575207424 |
|---|---|
| adam_text | Contents
Preface
v
Acknowledgments
vii
Index
of Notation
xi
1
Affine
Algebraic Varieties
1
1.1
Definition and Examples
.................. 2
1.2
The Zariski Topology
................... 6
1.3
Morphisms of
Affine
Algebraic Varieties
.......... 9
1.4
Dimension
..........................
ц
2
Algebraic Foundations
13
2.1
A Quick Review of Commutative Ring Theory
...... 13
2.2
Hubert s Basis Theorem
.................. 16
2.3
Hubert s
Nullstellensatz .................. 18
2.4
The Coordinate Ring
.................... 21
2.5
The Equivalence of Algebra and Geometry
........ 24
2.6
The Spectrum of a Ring
.................. 28
3
Projective Varieties
31
3.1
Projective Space
....................... 31
3.2
Projective Varieties
..................... 35
3.3
The Projective Closure of an
Affine
Variety
....... 38
χ
Contents
3.4
Morphisms of
Projective
Varieties
............. 41
3.5
Automorphisms of
Projective
Space
............ 45
4
Quasi-Projective Varieties
49
4.1
Quasi-Projective Varieties
................. 49
4.2
A Basis for the Zariski Topology
.............. 52
4.3
Regular Functions
...................... 54
5
Classical Constructions
59
5.1
Veronese Maps
........................ 59
5.2
Five Points Determine a Conic
............... 61
5.3
The
Segre
Map and Products of Varieties
......... 63
5.4
Grassmannians
....................... 67
5.5
Degree
............................ 70
5.6
The Hubert Function
.................... 77
6
Smoothness
81
6.1
The Tangent Space at a Point
............... 81
6.2
Smooth Points
........................ 87
6.3
Smoothness in Families
................... 91
6.4
Bertini s Theorem
...................... 94
6.5
The Gauss Mapping
..................... 97
7 Birational
Geometry
99
7.1
Resolution of Singularities
................. 99
7.2
Rational Maps
........................ 106
7.3 Birational
Equivalence
................... 108
7.4
Blowing Up Along an Ideal
................. 109
7.5
Hypersurfaces
........................ 113
7.6
The Classification Problems
................ 114
8
Maps to
Projective
Space
117
8.1
Embedding a Smooth Curve in Three-Space
....... 118
8.2
Vector Bundles and Line Bundles
............. 121
8.3
The Sections of a Vector Bundle
.............. 123
8.4
Examples of Vector Bundles
................ 125
8.5
Line Bundles and Rational Maps
............. 130
8.6
Very Ample Line Bundles
................. 134
A Sheaves and Abstract Algebraic Varieties
139
A.I Sheaves
............................ 139
A.2 Abstract Algebraic Varieties
................ 144
References
147
Index
151
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:43:07Z |
| institution | BVB |
| isbn | 0387989803 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009057227 |
| oclc_num | 318271025 |
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| physical | XVI, 161 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | An invitation to algebraic geometry Karen E. Smith ... New York [u.a.] Springer 2000 XVI, 161 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Geometría algebraica Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s DE-604 Smith, Karen E. 1965- Sonstige (DE-588)128408677 oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009057227&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | An invitation to algebraic geometry Geometría algebraica Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4001161-6 |
| title | An invitation to algebraic geometry |
| title_auth | An invitation to algebraic geometry |
| title_exact_search | An invitation to algebraic geometry |
| title_full | An invitation to algebraic geometry Karen E. Smith ... |
| title_fullStr | An invitation to algebraic geometry Karen E. Smith ... |
| title_full_unstemmed | An invitation to algebraic geometry Karen E. Smith ... |
| title_short | An invitation to algebraic geometry |
| title_sort | an invitation to algebraic geometry |
| topic | Geometría algebraica Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Geometría algebraica Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009057227&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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