The geometry of schemes:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2001
|
| Edition: | Corrected 2. printing |
| Series: | Graduate texts in mathematics
197 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 279 - 283 |
| Physical Description: | X, 294 S. graph. Darst. 25 cm |
| ISBN: | 0387986383 0387986375 |
Staff View
MARC
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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 |
| 250 | |a Corrected 2. printing | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
| 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 | ||
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Record in the Search Index
| _version_ | 1804130063558377472 |
|---|---|
| adam_text | Contents
I
1.1
1.1.1 Schemes as Sets
1.1.2
1.1.3
References for the Theory of Sheaves
1.1.4
1.2
1.2.1
1.2.2
1.2.3
1.2.4
Projective
1.3
1.3.1
1.3.2
1.3.3
1.4
II Examples
ILI
11.1.1
11.1.2 Local Schemes
II.2 Reduced Schemes over
viii Contents
П.З
11.3.1 Double Points..................... 58
11.3.2 Multiple Points .................... 62
Degree and Multiplicity
11.3.3
Primary Decomposition
П.
Limits
Examples
Flatness
II.3.5 Multiple Lines
II.4 Arithmetic Schemes
11.4.1 SpecZ
11.4.2 Spec of the Ring of Integers in a Number Field
11.4.3
11.4.4 A Conic over SpecZ
11.4.5 Double Points in A^
III
ULI
111.
111.
111.2 Proj of a Graded Ring
111.2.1 The Construction of Proj
111.2.2 Closed Subschemes of Proj
111.2.3 Global Proj
Proj of a Sheaf of Graded
The Projectivization
111.2.4 Tangent Spaces and Tangent Cones
Affine
Tangent Cones
111.2.5 Morphisms to
111.2.6 Graded Modules and Sheaves
111.2.7 Grassmannians
111.2.8 Universal Hypersurfaces
111.3 Invariants of
111.3.1 Hilbert Functions and Hubert Polynomials
111.3.2 Flatness II: Families of
111.3.3 Free Resolutions
111.3.4 Examples
Points in the Plane
Examples: Double Lines in General and in
111.3.5
Multiplicity of Intersections
111.3.6 Hilbert Series
Contents ix
IV Classical Constructions
IV.l Flexes of Plane Curves
IV.1.1 Definitions
IV.
IV.
IV.2 Blow-ups
IV.2.1 Definitions and Constructions
An Example: Blowing up the Plane
Definition of Blow-ups in General
The Blowup as Proj
Blow-ups along Regular Subschemas
IV.2.2 Some Classic Blow-Ups
IV.
Blowing Up a Double Point
Blowing Up Multiple Points
The j-Function
IV.2.4 Blow-ups of Arithmetic Schemes
IV.2.
IV.3
IV.3.1 Definitions
IV.3.2 Lines on Quadrics
Lines on a Smooth Quadric over an Algebraically
Closed Field
Lines on a Quadric Cone
A Quadric Degenerating to Two Planes
More Examples
IV.3.3 Lines on Cubic Surfaces
IV.4 Forms
V Local Constructions
V.I Images
V.I.I The Image of a Morphism of Schemes
V.1.2 Universal Formulas
V.1.3 Fitting Ideals and Fitting Images
Fitting Ideals
Fitting Images
V.2 Resultants
V.2.1 Definition of the Resultant
V.2.2 Sylvester s Determinant
V.3 Singular Schemes and Discriminants
V.3.1 Definitions
V.3.2 Discriminants
V.3.3 Examples
x
V.4
V.4.1 Definitions
V.4.2 Duals of Singular Curves
V.4.3 Curves with Multiple Components
V.5 Double Point Loci
VI Schemes and Functors
VI.
VI.l.l Open and Closed Subfunctors
VI.1.2
VI.1.3 Tangent Spaces to a Functor
VI.1.4 Group Schemes
VI.
VI.2.1 Characterization of Schemes among Functors
VI.2.2 Parameter Spaces
The Hubert Scheme
Examples of Hubert Schemes
Variations on the Hilbert Scheme Construction
VI.2.3 Tangent Spaces to Schemes in Terms of Their Func¬
tors of Points
Tangent Spaces to Hilbert Schemes
Tangent Spaces to
VI.2.4 Moduli Spaces
References
Index
|
| any_adam_object | 1 |
| author | Eisenbud, David 1947- Harris, Joe 1951- |
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| classification_tum | MAT 140f |
| ctrlnum | (OCoLC)166422927 (DE-599)BVBBV017214131 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Corrected 2. printing |
| format | Book |
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| id | DE-604.BV017214131 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:15:05Z |
| institution | BVB |
| isbn | 0387986383 0387986375 |
| language | English |
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| spelling | Eisenbud, David 1947- Verfasser (DE-588)139999671 aut The geometry of schemes David Eisenbud ; Joe Harris Corrected 2. printing New York [u.a.] Springer 2001 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 Esquemas larpcal Geometria algébrica larpcal Schema's gtt Schémas (Géométrie algébrique) Schémas (Géométrie algébrique) ram Schemes (Algebraic geometry) Schema Mathematik (DE-588)4205720-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Schema Mathematik (DE-588)4205720-6 s Algebraische Geometrie (DE-588)4001161-6 s DE-604 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=010373070&sequence=000003&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 Esquemas larpcal Geometria algébrica larpcal Schema's gtt Schémas (Géométrie algébrique) Schémas (Géométrie algébrique) ram Schemes (Algebraic geometry) Schema Mathematik (DE-588)4205720-6 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4205720-6 (DE-588)4001161-6 |
| 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 Esquemas larpcal Geometria algébrica larpcal Schema's gtt Schémas (Géométrie algébrique) Schémas (Géométrie algébrique) ram Schemes (Algebraic geometry) Schema Mathematik (DE-588)4205720-6 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Algebraïsche meetkunde Esquemas Geometria algébrica Schema's Schémas (Géométrie algébrique) Schemes (Algebraic geometry) Schema Mathematik Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010373070&sequence=000003&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 |