Algebraic geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
[2000]
|
| Edition: | [Nachdr.] |
| Series: | Graduate texts in mathematics
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 496 S. graph. Darst. |
| ISBN: | 0387902449 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV021831219 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 061128s2000 d||| |||| 00||| eng d | ||
| 020 | |a 0387902449 |9 0-387-90244-9 | ||
| 035 | |a (OCoLC)248436721 | ||
| 035 | |a (DE-599)BVBBV021831219 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-19 |a DE-739 | ||
| 084 | |a SK 240 |0 (DE-625)143226: |2 rvk | ||
| 100 | 1 | |a Hartshorne, Robin |d 1938- |e Verfasser |0 (DE-588)133225089 |4 aut | |
| 245 | 1 | 0 | |a Algebraic geometry |c Robin Hartshorne |
| 250 | |a [Nachdr.] | ||
| 264 | 1 | |a New York |b Springer |c [2000] | |
| 300 | |a XVI, 496 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 52 | |
| 650 | 4 | |a Algebraische Geometrie | |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)1071861417 |a Konferenzschrift |y 1974 |z Arcata Calif. |2 gnd-content | |
| 655 | 7 | |8 2\p |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
| 655 | 7 | |8 3\p |0 (DE-588)1071861417 |a Konferenzschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Graduate texts in mathematics |v 52 |w (DE-604)BV000000067 |9 52 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015043209&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015043209 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804135761369366528 |
|---|---|
| adam_text | Contents
Introduction
xiii
CHAPTER I
Varieties
1
1
Affine
Varieties
1
2
Projective
Varieties
8
3
Morphisms
14
4
Rational Maps
24
5
Nonsingular Varieties
31
6
Nonsingular Curves
39
7
Intersections in
Projective
Space
47
8
What Is Algebraic Geometry?
55
CHAPTER II
Schemes
60
1
Sheaves
60
2
Schemes
69
3
First Properties of Schemes
82
4
Separated and Proper Morphisms
95
5
Sheaves of Modules
108
6
Divisors
129
7
Projective Morphisms
149
8
Differentials
172
9
Formal Schemes
190
CHAPTER III
Cohomology
201
1 Derived Functors
202
2
Cohomology of Sheaves
206
3
Cohomology of a Noetherian
Affine
Scheme
213
4
Cech Cohomology
218
5
The Cohomology
of
Projective
Space
225
6
Ext
Groups and Sheaves
233
7
The
Serre
Duality Theorem
239
8
Higher Direct Images of Sheaves
250
9
Flat Morphisms
253
10
Smooth Morphisms
268
11
The Theorem on Formal Functions
276
12
The Semicontinuity Theorem
281
CHAPTER IV
Curves
293
1
Riemann-Roch Theorem
294
2
Hurwitz s Theorem
299
3
Embeddings in
Projective
Space
307
4
Elliptic Curves
316
5
The Canonical Embedding
340
6
Classification of Curves in P
349
CHAPTER V
Surfaces
356
1
Geometry on a Surface
357
2
Ruled Surfaces
369
3
Monoidal Transformations
386
4
The Cubic Surface in
F
395
5 Birational
Transformations
409
6
Classification of Surfaces
421
APPENDIX A
Intersection Theory
424
1
Intersection Theory
425
2
Properties of the Chow Ring
428
3
Chern Classes
429
4
The Riemann-Roch Theorem
431
5
Complements and Generalizations
434
APPENDIX
В
Transcendental Methods
438
1
The Associated Complex Analytic Space
438
2
Comparison of the Algebraic and Analytic Categories
440
3
When is a Compact Complex Manifold Algebraic?
441
4 Kahler
Manifolds
445
5
The Exponential Sequence
446
APPENDIX
С
The Weil Conjectures
449
1
The
Zeta
Function and the Weil Conjectures
449
2
History of Work on the Weil Conjectures
451
3
The
/-adic Cohomology
453
4
Cohomological Interpretation of the Weil Conjectures
454
Bibliography
459
Results from Algebra
470
Glossary of Notations
472
Index
478
|
| adam_txt |
Contents
Introduction
xiii
CHAPTER I
Varieties
1
1
Affine
Varieties
1
2
Projective
Varieties
8
3
Morphisms
14
4
Rational Maps
24
5
Nonsingular Varieties
31
6
Nonsingular Curves
39
7
Intersections in
Projective
Space
47
8
What Is Algebraic Geometry?
55
CHAPTER II
Schemes
60
1
Sheaves
60
2
Schemes
69
3
First Properties of Schemes
82
4
Separated and Proper Morphisms
95
5
Sheaves of Modules
108
6
Divisors
129
7
Projective Morphisms
149
8
Differentials
172
9
Formal Schemes
190
CHAPTER III
Cohomology
201
1 Derived Functors
202
2
Cohomology of Sheaves
206
3
Cohomology of a Noetherian
Affine
Scheme
213
4
Cech Cohomology
218
5
The Cohomology
of
Projective
Space
225
6
Ext
Groups and Sheaves
233
7
The
Serre
Duality Theorem
239
8
Higher Direct Images of Sheaves
250
9
Flat Morphisms
253
10
Smooth Morphisms
268
11
The Theorem on Formal Functions
276
12
The Semicontinuity Theorem
281
CHAPTER IV
Curves
293
1
Riemann-Roch Theorem
294
2
Hurwitz's Theorem
299
3
Embeddings in
Projective
Space
307
4
Elliptic Curves
316
5
The Canonical Embedding
340
6
Classification of Curves in P'
349
CHAPTER V
Surfaces
356
1
Geometry on a Surface
357
2
Ruled Surfaces
369
3
Monoidal Transformations
386
4
The Cubic Surface in
F
395
5 Birational
Transformations
409
6
Classification of Surfaces
421
APPENDIX A
Intersection Theory
424
1
Intersection Theory
425
2
Properties of the Chow Ring
428
3
Chern Classes
429
4
The Riemann-Roch Theorem
431
5
Complements and Generalizations
434
APPENDIX
В
Transcendental Methods
438
1
The Associated Complex Analytic Space
438
2
Comparison of the Algebraic and Analytic Categories
440
3
When is a Compact Complex Manifold Algebraic?
441
4 Kahler
Manifolds
445
5
The Exponential Sequence
446
APPENDIX
С
The Weil Conjectures
449
1
The
Zeta
Function and the Weil Conjectures
449
2
History of Work on the Weil Conjectures
451
3
The
/-adic Cohomology
453
4
Cohomological Interpretation of the Weil Conjectures
454
Bibliography
459
Results from Algebra
470
Glossary of Notations
472
Index
478 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Hartshorne, Robin 1938- |
| author_GND | (DE-588)133225089 |
| author_facet | Hartshorne, Robin 1938- |
| author_role | aut |
| author_sort | Hartshorne, Robin 1938- |
| author_variant | r h rh |
| building | Verbundindex |
| bvnumber | BV021831219 |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)248436721 (DE-599)BVBBV021831219 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | [Nachdr.] |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01853nam a2200433 cb4500</leader><controlfield tag="001">BV021831219</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">061128s2000 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387902449</subfield><subfield code="9">0-387-90244-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)248436721</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV021831219</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-739</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 240</subfield><subfield code="0">(DE-625)143226:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hartshorne, Robin</subfield><subfield code="d">1938-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)133225089</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algebraic geometry</subfield><subfield code="c">Robin Hartshorne</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">[Nachdr.]</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York</subfield><subfield code="b">Springer</subfield><subfield code="c">[2000]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 496 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">52</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraische Geometrie</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Geometrie</subfield><subfield code="0">(DE-588)4001161-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">1\p</subfield><subfield code="0">(DE-588)1071861417</subfield><subfield code="a">Konferenzschrift</subfield><subfield code="y">1974</subfield><subfield code="z">Arcata Calif.</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">2\p</subfield><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">3\p</subfield><subfield code="0">(DE-588)1071861417</subfield><subfield code="a">Konferenzschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebraische Geometrie</subfield><subfield code="0">(DE-588)4001161-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">52</subfield><subfield code="w">(DE-604)BV000000067</subfield><subfield code="9">52</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015043209&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-015043209</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| genre | 1\p (DE-588)1071861417 Konferenzschrift 1974 Arcata Calif. gnd-content 2\p (DE-588)4151278-9 Einführung gnd-content 3\p (DE-588)1071861417 Konferenzschrift gnd-content |
| genre_facet | Konferenzschrift 1974 Arcata Calif. Einführung Konferenzschrift |
| id | DE-604.BV021831219 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:57:22Z |
| indexdate | 2024-07-09T20:45:38Z |
| institution | BVB |
| isbn | 0387902449 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015043209 |
| oclc_num | 248436721 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-739 |
| owner_facet | DE-19 DE-BY-UBM DE-739 |
| physical | XVI, 496 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Hartshorne, Robin 1938- Verfasser (DE-588)133225089 aut Algebraic geometry Robin Hartshorne [Nachdr.] New York Springer [2000] XVI, 496 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 52 Algebraische Geometrie Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1974 Arcata Calif. gnd-content 2\p (DE-588)4151278-9 Einführung gnd-content 3\p (DE-588)1071861417 Konferenzschrift gnd-content Algebraische Geometrie (DE-588)4001161-6 s DE-604 Graduate texts in mathematics 52 (DE-604)BV000000067 52 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015043209&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hartshorne, Robin 1938- Algebraic geometry Graduate texts in mathematics Algebraische Geometrie Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)1071861417 (DE-588)4151278-9 |
| title | Algebraic geometry |
| title_auth | Algebraic geometry |
| title_exact_search | Algebraic geometry |
| title_exact_search_txtP | Algebraic geometry |
| title_full | Algebraic geometry Robin Hartshorne |
| title_fullStr | Algebraic geometry Robin Hartshorne |
| title_full_unstemmed | Algebraic geometry Robin Hartshorne |
| title_short | Algebraic geometry |
| title_sort | algebraic geometry |
| topic | Algebraische Geometrie Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Algebraische Geometrie Konferenzschrift 1974 Arcata Calif. Einführung Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015043209&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT hartshornerobin algebraicgeometry |