Introduction to algebraic curves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1999
|
| Ausgabe: | 4. [printing] |
| Schriftenreihe: | Translations of mathematical monographs
76 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Chines. übers. |
| Beschreibung: | X, 225 S. graph. Darst. |
| ISBN: | 0821845373 9780821845370 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to algebraic curves |c Phillip A. Griffiths |
| 250 | |a 4. [printing] | ||
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1999 | |
| 300 | |a X, 225 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 76 | |
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Datensatz im Suchindex
| _version_ | 1804137433374130176 |
|---|---|
| adam_text | Contents
Chapter I. Fundamental Concepts
1
§1.
Algebraic curves in the complex
projective
plane
ľ C
1
§2.
Riemann surfaces
4
§3.
Holomorphic and meromorphic functions
12
§4.
Holomorphic and meromorphic differentials
15
§5.
Differential forms
19
§6.
The
Poincaré-Hopf
formula
22
§7.
Complex manifolds
24
§8.
Algebraic varieties
31
§9.
Smooth points, tangent spaces and the implicit function
theorem
36
§10.
Holomorphic mappings from compact Riemann surfaces
into complex
projective
spaces
46
Chapter II. The Normalization Theorem and its Applications
53
§1.
Singularities of plane algebraic curves
53
§2.
The connectedness of irreducible plane algebraic curves
56
§3.
The concept of normalization
66
§4.
The
Weierstrass
polynomial
68
§5.
The local structure of plane algebraic curves
75
§6.
The completion of the proof of the normalization theorem
81
§7.
Divisors, intersection numbers and
Bezouťs
theorem
82
§8.
Ramification divisors and the Riemann-Hurwitz formula
90
§9.
The genus formula
95
Chapter III. The Riemann-Roch Theorem
99
§1.
Preliminaries
99
§2.
The dimension of
Ω1
í C
і
102
§3.
Two important theorems
109
§4.
The Riemann inequality
112
§5.
The Riemann-Roch theorem 1
18
x
CONTENTS
Chapter IV. Applications of the Riemann-Roch Theorem
125
§1.
The case of genus
0 125
§2.
The case of genus
1 126
§3.
Canonical maps
132
§4.
Hyperelliptic compact Riemann surfaces
137
§5.
The case of genus
2 144
§6.
The case of genus
3 145
§7.
The case of genus
4 148
Chapter V. Abel s Theorem and Its Applications
153
§1.
The Jacobian variety and Abel s theorem
153
§2.
Differentials of the third kind
158
§3.
The Riemann bilinear relations
168
§4.
The Jacobi inversion theorem
177
§5.
Applications of Abel s theorem
192
Test Problems I. (Chapters I and II)
207
Test Problems II. (Chapters III, IV, and V)
209
Appendix. On a General Fact
213
Annotated Bibliography
217
Index
221
|
| adam_txt |
Contents
Chapter I. Fundamental Concepts
1
§1.
Algebraic curves in the complex
projective
plane
ľ'C
1
§2.
Riemann surfaces
4
§3.
Holomorphic and meromorphic functions
12
§4.
Holomorphic and meromorphic differentials
15
§5.
Differential forms
19
§6.
The
Poincaré-Hopf
formula
22
§7.
Complex manifolds
24
§8.
Algebraic varieties
31
§9.
Smooth points, tangent spaces and the implicit function
theorem
36
§10.
Holomorphic mappings from compact Riemann surfaces
into complex
projective
spaces
46
Chapter II. The Normalization Theorem and its Applications
53
§1.
Singularities of plane algebraic curves
53
§2.
The connectedness of irreducible plane algebraic curves
56
§3.
The concept of normalization
66
§4.
The
Weierstrass
polynomial
68
§5.
The local structure of plane algebraic curves
75
§6.
The completion of the proof of the normalization theorem
81
§7.
Divisors, intersection numbers and
Bezouťs
theorem
82
§8.
Ramification divisors and the Riemann-Hurwitz formula
90
§9.
The genus formula
95
Chapter III. The Riemann-Roch Theorem
99
§1.
Preliminaries
99
§2.
The dimension of
Ω1
í C
і
102
§3.
Two important theorems
109
§4.
The Riemann inequality
112
§5.
The Riemann-Roch theorem 1
18
x
CONTENTS
Chapter IV. Applications of the Riemann-Roch Theorem
125
§1.
The case of genus
0 125
§2.
The case of genus
1 126
§3.
Canonical maps
132
§4.
Hyperelliptic compact Riemann surfaces
137
§5.
The case of genus
2 144
§6.
The case of genus
3 145
§7.
The case of genus
4 148
Chapter V. Abel's Theorem and Its Applications
153
§1.
The Jacobian variety and Abel's theorem
153
§2.
Differentials of the third kind
158
§3.
The Riemann bilinear relations
168
§4.
The Jacobi inversion theorem
177
§5.
Applications of Abel's theorem
192
Test Problems I. (Chapters I and II)
207
Test Problems II. (Chapters III, IV, and V)
209
Appendix. On a "General Fact"
213
Annotated Bibliography
217
Index
221 |
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| institution | BVB |
| isbn | 0821845373 9780821845370 |
| language | English |
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| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Griffiths, Phillip 1938- Verfasser (DE-588)131881434 aut Introduction to algebraic curves Phillip A. Griffiths 4. [printing] Providence, RI American Math. Soc. 1999 X, 225 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 76 Aus dem Chines. übers. Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 s Algebraische Kurve (DE-588)4001165-3 s 1\p DE-604 Translations of mathematical monographs 76 (DE-604)BV000002394 76 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016357818&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 | Griffiths, Phillip 1938- Introduction to algebraic curves Translations of mathematical monographs Algebraische Kurve (DE-588)4001165-3 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| subject_GND | (DE-588)4001165-3 (DE-588)4049991-1 |
| title | Introduction to algebraic curves |
| title_auth | Introduction to algebraic curves |
| title_exact_search | Introduction to algebraic curves |
| title_exact_search_txtP | Introduction to algebraic curves |
| title_full | Introduction to algebraic curves Phillip A. Griffiths |
| title_fullStr | Introduction to algebraic curves Phillip A. Griffiths |
| title_full_unstemmed | Introduction to algebraic curves Phillip A. Griffiths |
| title_short | Introduction to algebraic curves |
| title_sort | introduction to algebraic curves |
| topic | Algebraische Kurve (DE-588)4001165-3 gnd Riemannsche Fläche (DE-588)4049991-1 gnd |
| topic_facet | Algebraische Kurve Riemannsche Fläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016357818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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