An invitation to algebraic geometry:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2004
|
| Ausgabe: | Corr. print., 2. print. |
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 161 S. Ill., graph. Darst. |
| ISBN: | 0387989803 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV019825551 | ||
| 003 | DE-604 | ||
| 005 | 20100721 | ||
| 007 | t | ||
| 008 | 050530s2004 ad|| |||| 00||| eng d | ||
| 020 | |a 0387989803 |9 0-387-98980-3 | ||
| 035 | |a (OCoLC)493748959 | ||
| 035 | |a (DE-599)BVBBV019825551 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-824 |a DE-355 |a DE-384 |a DE-19 |a DE-188 | ||
| 084 | |a SK 240 |0 (DE-625)143226: |2 rvk | ||
| 084 | |a SK 840 |0 (DE-625)143261: |2 rvk | ||
| 084 | |a MAT 140f |2 stub | ||
| 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 | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 7 | |a Géométrie algébrique |2 ram | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Smith, Karen E. |d 1965- |e Sonstige |0 (DE-588)128408677 |4 oth | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-013150742 | ||
Datensatz im Suchindex
| _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
|
| any_adam_object | 1 |
| author_GND | (DE-588)128408677 |
| building | Verbundindex |
| bvnumber | BV019825551 |
| classification_rvk | SK 240 SK 840 |
| classification_tum | MAT 140f |
| ctrlnum | (OCoLC)493748959 (DE-599)BVBBV019825551 |
| discipline | Mathematik |
| edition | Corr. print., 2. print. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01462nam a2200385 c 4500</leader><controlfield tag="001">BV019825551</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20100721 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">050530s2004 ad|| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387989803</subfield><subfield code="9">0-387-98980-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)493748959</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV019825551</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-824</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-188</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="084" ind1=" " ind2=" "><subfield code="a">SK 840</subfield><subfield code="0">(DE-625)143261:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 140f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">An invitation to algebraic geometry</subfield><subfield code="c">Karen E. Smith ...</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Corr. print., 2. print.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2004</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 161 S.</subfield><subfield code="b">Ill., 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="0" ind2=" "><subfield code="a">Universitext</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Géométrie algébrique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, Algebraic</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="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="700" ind1="1" ind2=" "><subfield code="a">Smith, Karen E.</subfield><subfield code="d">1965-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)128408677</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</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=013150742&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:BVB01-013150742</subfield></datafield></record></collection> |
| 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 |
| open_access_boolean | |
| owner | DE-824 DE-355 DE-BY-UBR DE-384 DE-19 DE-BY-UBM DE-188 |
| owner_facet | DE-824 DE-355 DE-BY-UBR DE-384 DE-19 DE-BY-UBM DE-188 |
| physical | XVI, 161 S. Ill., graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| 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 |
| work_keys_str_mv | AT smithkarene aninvitationtoalgebraicgeometry |