An introduction to Riemann surfaces, algebraic curves and moduli spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1989
|
| Series: | Lecture notes in physics
322 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XV, 148 S. graph. Darst. |
| ISBN: | 354050124X 038750124X |
Staff View
MARC
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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 |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1989 | |
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| 650 | 7 | |a Riemann, Surfaces de |2 ram | |
| 650 | 7 | |a Riemann-vlakken |2 gtt | |
| 650 | 4 | |a Curves, Algebraic | |
| 650 | 4 | |a Moduli theory | |
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Record in the Search Index
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| adam_text | Table of Contents
Introduction
Introduction from a Physicist s Viewpoint (by Ian McArthur)
§1. Manifolds 1
(a) Generalities 1
(b) Complex Manifolds 4
(c) The Classification Problem 7
§ 2. Topology of Riemann Surfaces 10
(a) Fundamental Group 10
(b) Simplicial Homology 14
(c) Universal Covering Space 21
§ 3. Analytic Structure 25
(a) Holomorphic and Meromorphic Functions 25
(b) Divisors and the Theorem of Riemann Roch 30
(c) Meromorphic Functions on the Torus 33
§ 4. Differentials and Integration 37
(a) Tangent Space and Differentials 37
(b) Differential Forms of Second Order 43
(c) Integration 45
§ 5. Tori and Jacobians 48
(a) Higher Dimensional Tori 48
(b) Jacobians 51
§ 6. Projective Varieties 56
(a) Generalities 56
(b) Embedding of 1 Dimensional Tori 61
(c) Theta Functions 62
§ 7. Moduli Space of Curves 67
(a) The Definition 67
(b) Methods of Construction 70
(c) The Geometry of the Moduli Space and the Compactification ... 76
IV
§ 8. Vector Bundles, Sheaves and Cohomology 85
(a) Vector Bundles 85
(b) Sheaves 90
(c) Cohomology 94
§ 9. The Theorem of Riemann Roch for Line Bundles 101
(a) Divisors and Line Bundles 101
(b) An Application: The Krichever Novikov Algebra 109
§10. The Mumford Isomorphism on the Moduli Space 119
(a) The Mumford Isomorphism 119
(b) The Grothendieck Riemann Roch Theorem 125
Appendix : p adic Numbers 134
Index 144
|
| any_adam_object | 1 |
| author | Schlichenmaier, Martin |
| author_facet | Schlichenmaier, Martin |
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| author_sort | Schlichenmaier, Martin |
| author_variant | m s ms |
| building | Verbundindex |
| bvnumber | BV001827163 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA333 |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 306f MAT 140f |
| ctrlnum | (OCoLC)18960059 (DE-599)BVBBV001827163 |
| dewey-full | 515/.223 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.223 |
| dewey-search | 515/.223 |
| dewey-sort | 3515 3223 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:36:22Z |
| institution | BVB |
| isbn | 354050124X 038750124X |
| language | English |
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| physical | XV, 148 S. graph. Darst. |
| publishDate | 1989 |
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| series2 | Lecture notes in physics |
| spelling | Schlichenmaier, Martin Verfasser aut An introduction to Riemann surfaces, algebraic curves and moduli spaces Martin Schlichenmaier Berlin [u.a.] Springer 1989 XV, 148 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 322 Literaturangaben Algebraïsche krommen gtt Courbes algébriques ram Modules, Théorie des ram Moduli spaces gtt Riemann, Surfaces de ram Riemann-vlakken gtt Curves, Algebraic Moduli theory Riemann surfaces Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Modulraum (DE-588)4183462-8 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Modultheorie (DE-588)4170336-4 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 s Algebraische Geometrie (DE-588)4001161-6 s DE-604 Modultheorie (DE-588)4170336-4 s Algebraische Kurve (DE-588)4001165-3 s Modulraum (DE-588)4183462-8 s 1\p DE-604 Lecture notes in physics 322 (DE-604)BV000003166 322 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001218379&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 |
| spellingShingle | Schlichenmaier, Martin An introduction to Riemann surfaces, algebraic curves and moduli spaces Lecture notes in physics Algebraïsche krommen gtt Courbes algébriques ram Modules, Théorie des ram Moduli spaces gtt Riemann, Surfaces de ram Riemann-vlakken gtt Curves, Algebraic Moduli theory Riemann surfaces Algebraische Geometrie (DE-588)4001161-6 gnd Modulraum (DE-588)4183462-8 gnd Algebraische Kurve (DE-588)4001165-3 gnd Modultheorie (DE-588)4170336-4 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4183462-8 (DE-588)4001165-3 (DE-588)4170336-4 (DE-588)4049991-1 |
| 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_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 | Algebraïsche krommen gtt Courbes algébriques ram Modules, Théorie des ram Moduli spaces gtt Riemann, Surfaces de ram Riemann-vlakken gtt Curves, Algebraic Moduli theory Riemann surfaces Algebraische Geometrie (DE-588)4001161-6 gnd Modulraum (DE-588)4183462-8 gnd Algebraische Kurve (DE-588)4001165-3 gnd Modultheorie (DE-588)4170336-4 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| topic_facet | Algebraïsche krommen Courbes algébriques Modules, Théorie des Moduli spaces Riemann, Surfaces de Riemann-vlakken Curves, Algebraic Moduli theory Riemann surfaces Algebraische Geometrie Modulraum Algebraische Kurve Modultheorie Riemannsche Fläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001218379&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
| work_keys_str_mv | AT schlichenmaiermartin anintroductiontoriemannsurfacesalgebraiccurvesandmodulispaces |