A scrapbook of complex curve theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2003
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate studies in mathematics
55 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 188 S. graph. Darst. |
| ISBN: | 0821833073 |
Internformat
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| 245 | 1 | 0 | |a A scrapbook of complex curve theory |c C. Herbert Clemens |
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| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2003 | |
| 300 | |a XI, 188 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804132875626348544 |
|---|---|
| adam_text | Contents
Preface to the Second Edition vii
Preface ix
Notation xi
Chapter One • Conies
1.1. Hyperbola Shadows 1
1.2. Real Projective Space, The Unifier 5
1.3. Complex Projective Space, The Great Unifier 7
1.4. Linear Families of Conies 9
1.5. The Mystic Hexagon 11
1.6. The Cross Ratio 13
1.7. Cayley s Way of Doing Geometries of Constant Curvature 17
1.8. Through the Looking Glass 20
1.9. The Polar Curve 22
1.10. Perpendiculars in Hyperbolic Space 26
1.11. Circles in the K Geometry 30
1.12. Rational Points on Conies 33
Chapter Two • Cubks
2.1. Inflection Points 37
2.2. Normal Form for a Cubic 39
2.3. Cubics as Topological Groups 42
2.4. The Group of Rational Points on a Cubic 45
2.5. A Thought about Complex Conjugation 50
2.6. Some Meromorphic Functions on Cubics 51
2.7. Cross Ratio Revisited, A Moduli Space for Cubics 52
2.8. The Abelian Differential on a Cubic 53
2.9. The Elliptic Integral 55
2.10. The Picard Fuchs Equation 58
2.11. Rational Points on Cubics over Fp 62
2.12. Manin s Result: The Unity of Mathematics 65
2.13. Some Remarks on Serre Duality 69
v
vj Contents
Chapter Three • Theta Functions
3.1. Back to the Group Law on Cubics 73
3.2. You Can t Parametrize a Smooth Cubic Algebraically 75
3.3. Meromorphic Functions on Elliptic Curves 78
3.4. Meromorphic Functions on Plane Cubics 82
3.5. The Weierstrass p Function 85
3.6. Theta Null Values Give Moduli of Elliptic Curves 89
3.7. The Moduli Space of Level Two Structures on Elliptic Curves ... 92
3.8. Automorphisms of Elliptic Curves 95
3.9. The Moduli Space of Elliptic Curves 96
3.10. And So, By the Way, We Get Picard s Theorem 98
3.11. The Complex Structure of Jt 100
3.12. The ./ Invariant of an Elliptic Curve 102
3.13. Theta Nulls as Modular Forms 106
3.14. A Fundamental Domain for T2 109
3.15. Jacobi s Identity Ill
Chapter Four • The Jacobian Variety
4.1. Cohomology of a Complex Curve 113
4.2. Duality 116
4.3. The Chern Class of a Holomorphic Line Bundle 118
4.4. Abel s Theorem for Curves 122
4.5. The Classical Version of Abel s Theorem 127
4.6. The Jacobi Inversion Theorem 131
4.7. Back to Theta Functions 132
4.8. The Basic Computation 134
4.9. Riemann s Theorem 136
4.10. Linear Systems of Degree g 138
4.11. Riemann s Constant 139
4.12. Riemann s Singularities Theorem 142
Chapter Five • Quartics and Quintics
5.1. Topology of Plane Quartics 147
5.2. The Twenty Eight Bitangents 150
5.3. Where Are the Hyperelliptic Curves of Genus 3? 155
5.4. Quintics 158
Chapter Six • The Schottky Relation
6.1. Prym Varieties 161
6.2. Riemann s Theta Relation 164
6.3. Products of Pairs of Theta Functions 167
6.4. A Proportionality Theorem Relating Jacobians and Pryms 168
6.5. The Proportionality Theorem of Schottky Jung 173
6.6. The Schottky Relation 174
References 181
Additional References 183
Index 185
|
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| author | Clemens, Charles Herbert 1939- |
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| author_facet | Clemens, Charles Herbert 1939- |
| author_role | aut |
| author_sort | Clemens, Charles Herbert 1939- |
| author_variant | c h c ch chc |
| building | Verbundindex |
| bvnumber | BV019414575 |
| classification_rvk | SK 750 SK 240 |
| ctrlnum | (OCoLC)441092457 (DE-599)BVBBV019414575 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV019414575 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:59:46Z |
| institution | BVB |
| isbn | 0821833073 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012876421 |
| oclc_num | 441092457 |
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| owner_facet | DE-19 DE-BY-UBM DE-83 DE-188 |
| physical | XI, 188 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Clemens, Charles Herbert 1939- Verfasser (DE-588)172022444 aut A scrapbook of complex curve theory C. Herbert Clemens 2. ed. Providence, RI American Math. Soc. 2003 XI, 188 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 55 Thetafunktion (DE-588)4185175-4 gnd rswk-swf Komplexe Funktion (DE-588)4217733-9 gnd rswk-swf Komplexe algebraische Kurve (DE-588)4164890-0 gnd rswk-swf Jacobi-Mannigfaltigkeit (DE-588)4289324-0 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Komplexe algebraische Kurve (DE-588)4164890-0 s DE-604 Algebraische Kurve (DE-588)4001165-3 s Thetafunktion (DE-588)4185175-4 s Jacobi-Mannigfaltigkeit (DE-588)4289324-0 s Komplexe Funktion (DE-588)4217733-9 s 1\p DE-604 Graduate studies in mathematics 55 (DE-604)BV009739289 55 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012876421&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 | Clemens, Charles Herbert 1939- A scrapbook of complex curve theory Graduate studies in mathematics Thetafunktion (DE-588)4185175-4 gnd Komplexe Funktion (DE-588)4217733-9 gnd Komplexe algebraische Kurve (DE-588)4164890-0 gnd Jacobi-Mannigfaltigkeit (DE-588)4289324-0 gnd Algebraische Kurve (DE-588)4001165-3 gnd |
| subject_GND | (DE-588)4185175-4 (DE-588)4217733-9 (DE-588)4164890-0 (DE-588)4289324-0 (DE-588)4001165-3 |
| title | A scrapbook of complex curve theory |
| title_auth | A scrapbook of complex curve theory |
| title_exact_search | A scrapbook of complex curve theory |
| title_full | A scrapbook of complex curve theory C. Herbert Clemens |
| title_fullStr | A scrapbook of complex curve theory C. Herbert Clemens |
| title_full_unstemmed | A scrapbook of complex curve theory C. Herbert Clemens |
| title_short | A scrapbook of complex curve theory |
| title_sort | a scrapbook of complex curve theory |
| topic | Thetafunktion (DE-588)4185175-4 gnd Komplexe Funktion (DE-588)4217733-9 gnd Komplexe algebraische Kurve (DE-588)4164890-0 gnd Jacobi-Mannigfaltigkeit (DE-588)4289324-0 gnd Algebraische Kurve (DE-588)4001165-3 gnd |
| topic_facet | Thetafunktion Komplexe Funktion Komplexe algebraische Kurve Jacobi-Mannigfaltigkeit Algebraische Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012876421&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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