An introduction to Riemann surfaces, algebraic curves and moduli spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Edition: | 2. ed. |
| Series: | Theoretical and mathematical physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 217 S. graph. Darst. |
| ISBN: | 9783540711742 3540711740 |
Staff View
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| 100 | 1 | |a Schlichenmaier, Martin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to Riemann surfaces, algebraic curves and moduli spaces |c Martin Schlichenmaier |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XIII, 217 S. |b graph. Darst. | ||
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| 650 | 4 | |a Riemann, Surfaces de | |
| 650 | 4 | |a Curves, Algebraic | |
| 650 | 4 | |a Moduli theory | |
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Record in the Search Index
| _version_ | 1804137366082813952 |
|---|---|
| adam_text | Contents
Introduction
from a Physicist s Viewpoint
................. 1
1
Manifolds
.................................................. 7
1.1
Generalities
............................................. 7
1.2
Complex Manifolds
...................................... 9
1.3
The Classification Problem
............................... 13
Hints for Further Reading
..................................... 14
2
Topology of Riemann Surfaces
............................. 17
2.1
Fundamental Group
..................................... 17
2.2
Simplicial Homology
..................................... 21
2.3
Universal Covering Space
................................. 28
Hints for Further Reading
..................................... 29
3
Analytic Structure
......................................... 31
3.1
Holomorphic and Meromorphic Functions
.................. 31
3.2
Divisors and the Theorem of Riemann-Roch
................ 35
3.3
Meromorphic Functions on the Torus
...................... 38
Hints for Further Reading
..................................... 41
4
Differentials and Integration
............................... 43
4.1
Tangent Space and Differentials
........................... 43
4.2
Differential Forms of Second Order
........................ 48
4.3
Integration
............................................. 50
Hints for Further Reading
..................................... 52
5
Tori and Jacobians
........................................ 53
5.1
Higher Dimensional Tori
................................. 53
5.2
Jacobians
............................................... 55
Hints for Further Reading
..................................... 59
XII Contents
6
Projective
Varieties
........................................ 61
6.1
Generalities
............................................. 61
6.2
Embedding of One-Dimensional Tori
....................... 65
6.3
Theta Functions
......................................... 67
Hints for Further Reading
..................................... 69
7
Moduli Spaces of Curves
.................................. 71
7.1
The Definition
.......................................... 71
7.2
Methods of Construction
................................. 74
7.3
The Geometry of the Moduli Space and Its Compactification
.. 78
Hints for Further Reading
..................................... 85
8
Vector Bundles, Sheaves and Cohomology
................. 87
8.1
Vector Bundles
.......................................... 87
8.2
Sheaves
................................................ 91
8.3
Cohomology
............................................ 95
Hints for Further Reading
.....................................100
9
The Theorem of Riemann-Roch for Line Bundles
..........103
9.1
Divisors and Line Bundles
................................103
9.2
An Application: The Krichever-Novikov Algebra
............109
Hints for Further Reading
.....................................117
10
The Mumford Isomorphism on the Moduli Space
..........119
10.1
The Mumford Isomorphism
...............................119
10.2
The Grothendieck-Riemann-Roch Theorem
................125
Hints for Further Reading
.....................................131
11
Modern Algebraic Geometry
..............................133
11.1
Varieties
...............................................133
11.2
The Spectrum of a Ring
..................................139
11.3
Homomorphisms
........................................146
11.4
Noncommutative
Spaces
..................................149
Hints for Further Reading
.....................................153
12
Schemes
...................................................155
12.1
Affine
Schemes
..........................................155
12.2
General Schemes
........................................159
12.3
The Structure Sheaf Or
..................................162
12.4
Examples of Schemes
....................................164
Hints for Further Reading
.....................................167
Contents XIII
13
Hodge Decomposition and
Kahler
Manifold
................169
13.1
Some Introductory Remarks on Mirror Symmetry
...........169
13.2
Compact Complex Manifolds and Hodge Decomposition
......171
13.3 Kahler
Manifolds
........................................177
13.4
Hodge Numbers of the
Projective
Space
....................181
Hints for Further Reading
.....................................182
14
Calabi-Yau Manifolds and Mirror Symmetry
..............183
14.1
Calabi-Yau Manifolds
....................................183
14.2
КЗ
Surfaces, Hypersurfaces and Complete Intersections
.......187
14.3
Geometric Mirror Symmetry
..............................192
14.4
Example of a Calabi-Yau Three-fold and Its Mirror: Results
of Givental
.............................................196
Hints for Further Reading
.....................................200
Appendix p-adic Numbers
.....................................203
Index
..........................................................213
|
| adam_txt |
Contents
Introduction
from a Physicist's Viewpoint
. 1
1
Manifolds
. 7
1.1
Generalities
. 7
1.2
Complex Manifolds
. 9
1.3
The Classification Problem
. 13
Hints for Further Reading
. 14
2
Topology of Riemann Surfaces
. 17
2.1
Fundamental Group
. 17
2.2
Simplicial Homology
. 21
2.3
Universal Covering Space
. 28
Hints for Further Reading
. 29
3
Analytic Structure
. 31
3.1
Holomorphic and Meromorphic Functions
. 31
3.2
Divisors and the Theorem of Riemann-Roch
. 35
3.3
Meromorphic Functions on the Torus
. 38
Hints for Further Reading
. 41
4
Differentials and Integration
. 43
4.1
Tangent Space and Differentials
. 43
4.2
Differential Forms of Second Order
. 48
4.3
Integration
. 50
Hints for Further Reading
. 52
5
Tori and Jacobians
. 53
5.1
Higher Dimensional Tori
. 53
5.2
Jacobians
. 55
Hints for Further Reading
. 59
XII Contents
6
Projective
Varieties
. 61
6.1
Generalities
. 61
6.2
Embedding of One-Dimensional Tori
. 65
6.3
Theta Functions
. 67
Hints for Further Reading
. 69
7
Moduli Spaces of Curves
. 71
7.1
The Definition
. 71
7.2
Methods of Construction
. 74
7.3
The Geometry of the Moduli Space and Its Compactification
. 78
Hints for Further Reading
. 85
8
Vector Bundles, Sheaves and Cohomology
. 87
8.1
Vector Bundles
. 87
8.2
Sheaves
. 91
8.3
Cohomology
. 95
Hints for Further Reading
.100
9
The Theorem of Riemann-Roch for Line Bundles
.103
9.1
Divisors and Line Bundles
.103
9.2
An Application: The Krichever-Novikov Algebra
.109
Hints for Further Reading
.117
10
The Mumford Isomorphism on the Moduli Space
.119
10.1
The Mumford Isomorphism
.119
10.2
The Grothendieck-Riemann-Roch Theorem
.125
Hints for Further Reading
.131
11
Modern Algebraic Geometry
.133
11.1
Varieties
.133
11.2
The Spectrum of a Ring
.139
11.3
Homomorphisms
.146
11.4
Noncommutative
Spaces
.149
Hints for Further Reading
.153
12
Schemes
.155
12.1
Affine
Schemes
.155
12.2
General Schemes
.159
12.3
The Structure Sheaf Or
.162
12.4
Examples of Schemes
.164
Hints for Further Reading
.167
Contents XIII
13
Hodge Decomposition and
Kahler
Manifold
.169
13.1
Some Introductory Remarks on Mirror Symmetry
.169
13.2
Compact Complex Manifolds and Hodge Decomposition
.171
13.3 Kahler
Manifolds
.177
13.4
Hodge Numbers of the
Projective
Space
.181
Hints for Further Reading
.182
14
Calabi-Yau Manifolds and Mirror Symmetry
.183
14.1
Calabi-Yau Manifolds
.183
14.2
КЗ
Surfaces, Hypersurfaces and Complete Intersections
.187
14.3
Geometric Mirror Symmetry
.192
14.4
Example of a Calabi-Yau Three-fold and Its Mirror: Results
of Givental
.196
Hints for Further Reading
.200
Appendix p-adic Numbers
.203
Index
.213 |
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| edition | 2. ed. |
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| id | DE-604.BV023105725 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:46:34Z |
| indexdate | 2024-07-09T21:11:09Z |
| institution | BVB |
| isbn | 9783540711742 3540711740 |
| language | English |
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| physical | XIII, 217 S. graph. Darst. |
| publishDate | 2007 |
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| publisher | Springer |
| record_format | marc |
| series2 | Theoretical and mathematical physics |
| spelling | Schlichenmaier, Martin Verfasser aut An introduction to Riemann surfaces, algebraic curves and moduli spaces Martin Schlichenmaier 2. ed. Berlin [u.a.] Springer 2007 XIII, 217 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Theoretical and mathematical physics Courbes algébriques Modules, Théorie des Riemann, Surfaces de Curves, Algebraic Moduli theory Riemann surfaces Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Modulraum (DE-588)4183462-8 gnd rswk-swf Modultheorie (DE-588)4170336-4 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 s Algebraische Kurve (DE-588)4001165-3 s Modulraum (DE-588)4183462-8 s DE-604 Algebraische Geometrie (DE-588)4001161-6 s 1\p DE-604 Modultheorie (DE-588)4170336-4 s 2\p DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016308400&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 |
| spellingShingle | Schlichenmaier, Martin An introduction to Riemann surfaces, algebraic curves and moduli spaces Courbes algébriques Modules, Théorie des Riemann, Surfaces de Curves, Algebraic Moduli theory Riemann surfaces Riemannsche Fläche (DE-588)4049991-1 gnd Modulraum (DE-588)4183462-8 gnd Modultheorie (DE-588)4170336-4 gnd Algebraische Kurve (DE-588)4001165-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4049991-1 (DE-588)4183462-8 (DE-588)4170336-4 (DE-588)4001165-3 (DE-588)4001161-6 |
| title | An introduction to Riemann surfaces, algebraic curves and moduli spaces |
| title_auth | An introduction to Riemann surfaces, algebraic curves and moduli spaces |
| title_exact_search | An introduction to Riemann surfaces, algebraic curves and moduli spaces |
| title_exact_search_txtP | An introduction to Riemann surfaces, algebraic curves and moduli spaces |
| title_full | An introduction to Riemann surfaces, algebraic curves and moduli spaces Martin Schlichenmaier |
| title_fullStr | An introduction to Riemann surfaces, algebraic curves and moduli spaces Martin Schlichenmaier |
| title_full_unstemmed | An introduction to Riemann surfaces, algebraic curves and moduli spaces Martin Schlichenmaier |
| title_short | An introduction to Riemann surfaces, algebraic curves and moduli spaces |
| title_sort | an introduction to riemann surfaces algebraic curves and moduli spaces |
| topic | Courbes algébriques Modules, Théorie des Riemann, Surfaces de Curves, Algebraic Moduli theory Riemann surfaces Riemannsche Fläche (DE-588)4049991-1 gnd Modulraum (DE-588)4183462-8 gnd Modultheorie (DE-588)4170336-4 gnd Algebraische Kurve (DE-588)4001165-3 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Courbes algébriques Modules, Théorie des Riemann, Surfaces de Curves, Algebraic Moduli theory Riemann surfaces Riemannsche Fläche Modulraum Modultheorie Algebraische Kurve Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016308400&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schlichenmaiermartin anintroductiontoriemannsurfacesalgebraiccurvesandmodulispaces |