An invitation to algebraic geometry:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York [u.a.]
Springer
2004
|
| Edition: | Corr. print., 2. print. |
| 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 ... |
| 250 | |a Corr. print., 2. print. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2004 | |
| 300 | |a XVI, 161 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Record in the Search Index
| _version_ | 1804133329918754816 |
|---|---|
| adam_text | Contents
Notes
for the Second Printing
v
Preface
vii
Acknowledgments
ix
Index of Notation
xv
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
.......................... 11
2
Algebraic Foundations
15
2.1
A Quick Review of Commutative Ring Theory
...... 15
2.2
Hubert s Basis Theorem
.................. 18
2.3
Hilbert s
Nullstellensatz .................. 20
2.4
The Coordinate Ring
.................... 23
2.5
The Equivalence of Algebra and Geometry
........ 26
2.6
The Spectrum of a Ring
.................. 30
3
Projective
Varieties
33
3.1
Projective
Space
....................... 33
3.2
Projective
Varieties
..................... 37
xii Contents
3.3
The Projectie
Closure of an
Affine
Variety
....... 41
3.4
Morphisms of Project.ive Varieties
............. 44
3.5
Automorphisms of
Projective
Space
............ 47
4
Quasi-Projective Varieties
51
4.1
Quasi-Projective Varieties
................. 51
4.2
A Basis for the Zariski Topology
.............. 55
4.3
Regular Functions
...................... 56
5
Classical Constructions
63
5.1
Veronese Maps
........................ 63
5.2
Five Points Determine a Conic
............... 65
5.3
The
Segre
Map and Products of Varieties
......... 67
5.4
Grassmannians
....................... 71
5.5
Degree
............................ 74
5.6
The Hubert Function
.................... 81
6
Smoothness
85
6.1
The Tangent Space at a Point
............... 85
6.2
Smooth Points
........................ 92
6.3
Smoothness in Families
................... 96
6.4
Bertini
s Theorem
...................... 99
6.5
The Gauss Mapping
..................... 102
7 Birational
Geometry
105
7.1
Resolution of Singularities
................. 105
7.2
Rational Maps
........................ 112
7.3 Birational
Equivalence
................... 114
7.4
Blowing Up Along an Ideal
................. 115
7.5
Hypersurfaces
........................ 119
7.6
The Classification Problems
................ 120
8
Maps to
Projective
Space
123
8.1
Embedding a Smooth Curve in Three-Space
....... 124
8.2
Vector Bundles and Line Bundles
............. 127
8.3
The Sections of a Vector Bundle
.............. 129
8.4
Examples of Vector Bundles
................ 131
8.5
Line Bundles and Rational Maps
............. 136
8.6
Very Ample Line Bundles
................. 141
A Sheaves and Abstract Algebraic Varieties
145
A.I Sheaves
............................ 145
A.
2
Abstract Algebraic Varieties
................ 150
References
153
Contents xiii
Index 157
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| edition | Corr. print., 2. print. |
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| id | DE-604.BV019825551 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:07:00Z |
| institution | BVB |
| isbn | 0387989803 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013150742 |
| oclc_num | 493748959 |
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| physical | XVI, 161 S. Ill., graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
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| series2 | Universitext |
| spelling | An invitation to algebraic geometry Karen E. Smith ... Corr. print., 2. print. New York [u.a.] Springer 2004 XVI, 161 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Géométrie algébrique ram Geometry, Algebraic 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=013150742&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | An invitation to algebraic geometry Géométrie algébrique ram Geometry, Algebraic 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 | 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=013150742&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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