The geometry of schemes:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2000
|
| Schriftenreihe: | Graduate texts in mathematics
197 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 279 - 283 |
| Beschreibung: | X, 294 S. graph. Darst. 25 cm |
| ISBN: | 0387986383 0387986375 |
Internformat
MARC
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| 001 | BV013062789 | ||
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| 100 | 1 | |a Eisenbud, David |d 1947- |e Verfasser |0 (DE-588)139999671 |4 aut | |
| 245 | 1 | 0 | |a The geometry of schemes |c David Eisenbud ; Joe Harris |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2000 | |
| 300 | |a X, 294 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 197 | |
| 500 | |a Literaturverz. S. 279 - 283 | ||
| 650 | 7 | |a Algebraïsche meetkunde |2 gtt | |
| 650 | 7 | |a Schema's |2 gtt | |
| 650 | 4 | |a Schémas (Géométrie algébrique) | |
| 650 | 7 | |a Schémas (Géométrie algébrique) |2 ram | |
| 650 | 4 | |a Schemes (Algebraic geometry) | |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Schema |g Mathematik |0 (DE-588)4205720-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Schema |g Mathematik |0 (DE-588)4205720-6 |D s |
| 689 | 1 | 1 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Harris, Joe |d 1951- |e Verfasser |0 (DE-588)112574718 |4 aut | |
| 830 | 0 | |a Graduate texts in mathematics |v 197 |w (DE-604)BV000000067 |9 197 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008900592 | ||
Datensatz im Suchindex
| _version_ | 1804127761600610304 |
|---|---|
| adam_text | Contents
Introduction
1
I Basic Definitions
7
1.1
Affine
Schemes
......................... 7
1.1.1
Schemes as Sets
.................... 9
1.1.2
Schemes as
Topologicei
Spaces
............ 10
1.1.3
An Interlude on Sheaf Theory
............ 11
References for the Theory of Sheaves
........ 18
1.1.4
Schemes as Schemes (Structure Sheaves)
...... 18
1.2
Schemes in General
...................... 21
1.2.1
Subschemes
...................... 23
1.2.2
The Local Ring at a Point
.............. 26
1.2.3
Morphisms
....................... 28
1.2.4
The Gluing Construction
............... 33
Projective
Space
.................... 34
1.3
Relative Schemes
........................ 35
1.3.1
Fibered Products
................... 35
1.3.2
The Category of S-Schemes
............. 39
1.3.3
Global Spec
...................... 40
1.4
The Functor of Points
..................... 42
II Examples
47
ILI
Reduced Schemes over Algebraically Closed Fields
..... 47
11.1.1
Affine
Spaces
...................... 47
11.1.2 Local Schemes
..................... 50
II.2 Reduced Schemes over
Non-
Algebraically Closed Fields
. . 53
viii Contents
П.
3
Nonreduced Schemes
..................... 57
II.3.1 Double
Points
..................... 58
И.3.2
Multiple Points
.................... 62
Degree and Multiplicity
................ 65
11.3.3 Embedded Points
................... 66
Primary Decomposition
................ 67
11.3.4 Flat Families of Schemes
............... 70
Limits
.......................... 71
Examples
........................ 72
Flatness
........................ 75
11.3.5 Multiple Lines
..................... 80
II.4 Arithmetic Schemes
...................... 81
11.4.1 Spec
Z
......................... 82
11.4.2 Spec of the Ring of Integers in a Number Field
... 82
11.4.3
Affine
Spaces over Spec
Ћ
.............. 84
11.4.4 A Conic over Spec
Z
.................. 86
11.4.5 Double Points in k
.................. 88
III
Projective
Schemes
91
111.1 Attributes of Morphisms
................... 92
III.
1.1
Finiteness Conditions
................. 92
III.
1.2
Properness and Separation
.............. 93
111.2 Proj of a Graded Ring
..................... 95
111.2.1 The Construction of Proj
5.............. 95
111.2.2 Closed Subschemes of Proj
R
............. 100
111.2.3 Global Proj
...................... 101
Proj of a Sheaf of Graded 6X-Algebras
....... 101
The Projectivization
¥(£)
of a Coherent Sheaf
S
. 103
111.
2.4
Tangent Spaces and Tangent Cones
......... 104
Affine
and
Projective
Tangent Spaces
........ 104
Tangent Cones
..................... 106
111.2.5 Morphisms to
Projective
Space
............ 110
111.2.6 Graded Modules and Sheaves
............. 118
111.2.7 Grassmannians
..................... 119
111.
2.8
Universal Hypersurfaces
................ 122
111.3 Invariants of
Projective
Schemes
............... 124
III.3.1 Hubert Functions and Hilbert Polynomials
..... 125
IIL3.2 Flatness II: Families of
Projective
Schemes
..... 125
111.3.3 Free Resolutions
.................... 127
111.3.4 Examples
........................ 130
Points in the Plane
.................. 130
Examples: Double Lines in General and in P^
. . . 136
111.3.5
Bézouťs
Theorem
................... 140
Multiplicity of Intersections
.............. 146
111.3.6 Hilbert Series
..................... 149
Contents ix
IV Classical Constructions
151
IV.l Flexes of Plane Curves
....................151
IV.1.1 Definitions
....................... 151
IV.1.2 Flexes on Singular Curves
.............. 155
IV.
1.3
Curves with Multiple Components
.......... 156
IV.2 Blow-ups
............................ 162
IV.2.1 Definitions and Constructions
............ 162
An Example: Blowing up the Plane
......... 163
Definition of Blow-ups in General
.......... 164
The Blowup as Proj
.................. 169
Blow-ups along Regular Subschemes
......... 171
IV.2.2 Some Classic Blow-Ups
................ 173
IV.2.3 Blow-ups along Nonreduced Schemes
........ 179
Blowing Up a Double Point
.............. 179
Blowing Up Multiple Points
............. 181
The j-Function
.................... 183
IV.2.4 Blow-ups of Arithmetic Schemes
........... 184
IV.2.5 Project: Quadric and Cubic Surfaces as Blow-ups
. 190
IV.3
Fano
Schemes
.......................... 192
IV.3.1 Definitions
....................... 192
IV.3.2 Lines on Quadrics
................... 194
Lines on a Smooth Quadric over an Algebraically
Closed Field
..................... 194
Lines on a Quadric Cone
............... 196
A Quadric Degenerating to Two Planes
....... 198
More Examples
.................... 201
IV.3.3 Lines on Cubic Surfaces
................ 201
IV.4 Forms
.............................. 204
V Local Constructions
209
V.I Images
............................. 209
V.I.I The Image of a Morphism of Schemes
........ 209
V.1.2 Universal Formulas
.................. 213
V.1.3 Fitting Ideals and Fitting Images
.......... 219
Fitting Ideals
...................... 219
Fitting Images
..................... 221
V.2 Resultants
........................... 222
V.2.1 Definition of the Resultant
.............. 222
V.2.2 Sylvester s Determinant
................ 224
V.3 Singular Schemes and Discriminants
............. 230
V.3.1 Definitions
....................... 230
V.3.2 Discriminants
..................... 232
V.3.3 Examples
........................ 234
χ
Contents
V.4
Dual Curves
.......................... 240
V.4.1 Definitions
....................... 240
V.4.2 Duals of Singular Curves
............... 242
V.4.3 Curves with Multiple Components
.......... 242
V.5 Double Point Loci
....................... 246
VI Schemes and Functors
251
VI.l The Functor of Points
..................... 252
VI.
1.1
Open and Closed Subfunctors
............ 254
VI.l.
2
.ríľ-Rational
Points
................... 256
VI.
1.3
Tangent Spaces to a Functor
............. 256
VI.1.4 Group Schemes
.................... 258
VI.
2
Characterization of a Space by its Functor of Points
.... 259
VI.2.1 Characterization of Schemes among Functors
.... 259
VI.2.2 Parameter Spaces
................... 262
The Hilbert Scheme
.................. 262
Examples of Hilbert Schemes
............. 264
Variations on the Hilbert Scheme Construction
. . . 265
VI.2.3 Tangent Spaces to Schemes in Terms of Their Func¬
tors of Points
...................... 267
Tangent Spaces to Hilbert Schemes
......... 267
Tangent Spaces to
Fano
Schemes
........... 271
VI.2.4 Moduli Spaces
..................... 274
References
279
Index
285
|
| any_adam_object | 1 |
| author | Eisenbud, David 1947- Harris, Joe 1951- |
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| ctrlnum | (OCoLC)247093719 (DE-599)BVBBV013062789 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:38:29Z |
| institution | BVB |
| isbn | 0387986383 0387986375 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008900592 |
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| physical | X, 294 S. graph. Darst. 25 cm |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Eisenbud, David 1947- Verfasser (DE-588)139999671 aut The geometry of schemes David Eisenbud ; Joe Harris New York [u.a.] Springer 2000 X, 294 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 197 Literaturverz. S. 279 - 283 Algebraïsche meetkunde gtt Schema's gtt Schémas (Géométrie algébrique) Schémas (Géométrie algébrique) ram Schemes (Algebraic geometry) Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Schema Mathematik (DE-588)4205720-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s DE-604 Schema Mathematik (DE-588)4205720-6 s Harris, Joe 1951- Verfasser (DE-588)112574718 aut Graduate texts in mathematics 197 (DE-604)BV000000067 197 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008900592&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eisenbud, David 1947- Harris, Joe 1951- The geometry of schemes Graduate texts in mathematics Algebraïsche meetkunde gtt Schema's gtt Schémas (Géométrie algébrique) Schémas (Géométrie algébrique) ram Schemes (Algebraic geometry) Algebraische Geometrie (DE-588)4001161-6 gnd Schema Mathematik (DE-588)4205720-6 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4205720-6 |
| title | The geometry of schemes |
| title_auth | The geometry of schemes |
| title_exact_search | The geometry of schemes |
| title_full | The geometry of schemes David Eisenbud ; Joe Harris |
| title_fullStr | The geometry of schemes David Eisenbud ; Joe Harris |
| title_full_unstemmed | The geometry of schemes David Eisenbud ; Joe Harris |
| title_short | The geometry of schemes |
| title_sort | the geometry of schemes |
| topic | Algebraïsche meetkunde gtt Schema's gtt Schémas (Géométrie algébrique) Schémas (Géométrie algébrique) ram Schemes (Algebraic geometry) Algebraische Geometrie (DE-588)4001161-6 gnd Schema Mathematik (DE-588)4205720-6 gnd |
| topic_facet | Algebraïsche meetkunde Schema's Schémas (Géométrie algébrique) Schemes (Algebraic geometry) Algebraische Geometrie Schema Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008900592&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT eisenbuddavid thegeometryofschemes AT harrisjoe thegeometryofschemes |