Compact Riemann surfaces and algebraic curves:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore ; New Jersey ; London ; Hong Kong
World Scientific
1988
|
| Series: | Series in pure mathematics
10 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | viii, 174 Seiten |
| ISBN: | 9971507587 |
Staff View
MARC
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Preface v
Chapter 0. Topological Preliminaries 1
§ 1. Simplicial Homology 1
§2. Singular Homology and Relative Homology 4
§3. Cellular Homology 8
§4. De Rham Cohomology 11
§5. Cohomology with a Coefficient Sheaf 17
Chapter I. Commutative Algebra: An Introduction 25
§ 1. Affine and Projective Varieties 25
§2. Closed Ideals and Varieties 28
§3. Prime Ideals and Irreducible Varieties 31
§4. An Algebraic Interlude 35
§5. Coordinate Rings 42
§6. Dimension Theory 47
§7. Intersection Numbers 53
Chapter II. Singular Plane Curves 57
§ 1. Systems of Plane Curves 57
§2. Singular Points 59
§3. The Dual Curve 62
§4. The Classical Pliicker Formulae 64
Chapter III. Divisors on a Compact Complex Manifold 69
§ 1. Chern Classes of line Bundles 70
§2. Divisors and Holomorphic Line Bundles 73
§3. Linear Systems of Divisors 80
§4. Linear Systems on a Compact Riemann Surface and
Holomorphic Maps 83
§5. Examples: Rational and Elliptic Curves 88
vii
Chapter IV. Compact Riemann Surfaces 93
§ 1. The Hodge Theorem and Its Consequences 93
§2. Intersection Theory 99
§3. The Jacobian Variety and Abel s Theorem 105
§4. The Riemann Roch Theorem and the Canonical Embedding 114
§5. Hyperelliptic Riemann Surfaces and the Weierstrass Points 122
§6. Some Remarks on Holomorphic Maps 128
Chapter V. Geometry of Projective Curves 133
§ 1. Local Hermitian Geometry 133
§2. Singular Metrics on a Riemann Surface 139
§3. The Complex Flag Manifold 143
§4. Metric Geometry of Projective Curves 146
§5. Associated Curves and Horizontal Curves 150
§6. Plucker Formulae for Projective Algebraic Curve 153
§7. Harmonic Maps from a Compact Riemann Surface 156
Chapter VI. A Brief Look at Algebraic Surfaces 161
§1. The Intersection Form 161
§2. Blows Ups and Rational Maps 164
§3. The Kodaira Dimension of an Algebraic Surface 167
Bibliography 171
viii
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| discipline | Mathematik |
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| id | DE-604.BV001343464 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:27:36Z |
| institution | BVB |
| isbn | 9971507587 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000812721 |
| oclc_num | 260179231 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-83 DE-11 DE-188 |
| physical | viii, 174 Seiten |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | World Scientific |
| record_format | marc |
| series | Series in pure mathematics |
| series2 | Series in pure mathematics |
| spelling | Yang, Kichoon 1955- (DE-588)172468841 aut Compact Riemann surfaces and algebraic curves Kichoon Yang Singapore ; New Jersey ; London ; Hong Kong World Scientific 1988 viii, 174 Seiten txt rdacontent n rdamedia nc rdacarrier Series in pure mathematics 10 Kompakter Riemannscher Raum (DE-588)4164858-4 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Kompakte Riemannsche Fläche (DE-588)4164852-3 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 s Kompakte Riemannsche Fläche (DE-588)4164852-3 s DE-604 Kompakter Riemannscher Raum (DE-588)4164858-4 s Series in pure mathematics 10 (DE-604)BV000016845 10 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000812721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yang, Kichoon 1955- Compact Riemann surfaces and algebraic curves Series in pure mathematics Kompakter Riemannscher Raum (DE-588)4164858-4 gnd Algebraische Kurve (DE-588)4001165-3 gnd Kompakte Riemannsche Fläche (DE-588)4164852-3 gnd |
| subject_GND | (DE-588)4164858-4 (DE-588)4001165-3 (DE-588)4164852-3 |
| title | Compact Riemann surfaces and algebraic curves |
| title_auth | Compact Riemann surfaces and algebraic curves |
| title_exact_search | Compact Riemann surfaces and algebraic curves |
| title_full | Compact Riemann surfaces and algebraic curves Kichoon Yang |
| title_fullStr | Compact Riemann surfaces and algebraic curves Kichoon Yang |
| title_full_unstemmed | Compact Riemann surfaces and algebraic curves Kichoon Yang |
| title_short | Compact Riemann surfaces and algebraic curves |
| title_sort | compact riemann surfaces and algebraic curves |
| topic | Kompakter Riemannscher Raum (DE-588)4164858-4 gnd Algebraische Kurve (DE-588)4001165-3 gnd Kompakte Riemannsche Fläche (DE-588)4164852-3 gnd |
| topic_facet | Kompakter Riemannscher Raum Algebraische Kurve Kompakte Riemannsche Fläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000812721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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