Ball and surface arithmetics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Braunschweig ; Wiesbaden
Vieweg
1998
|
| Schriftenreihe: | [Aspects of mathematics / E]
29 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 414 S. graph. Darst. |
| ISBN: | 3528065117 |
Internformat
MARC
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| 245 | 1 | 0 | |a Ball and surface arithmetics |c Rolf-Peter Holzapfel |
| 264 | 1 | |a Braunschweig ; Wiesbaden |b Vieweg |c 1998 | |
| 300 | |a XIII, 414 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a [Aspects of mathematics / E] |v 29 | |
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Datensatz im Suchindex
| _version_ | 1804126249996517376 |
|---|---|
| adam_text | ^___ V
Contents
1 Abelian Points 1
1.1 Cyclic Points 1
1.2 Graphs of Abelian Points 5
1.3 Geometric Interpretation 7
1.4 Derived Representations 10
1.5 The Differential Relation 15
1.6 Stepwise Resolutions of Cyclic Points 19
1.7 Continued Fractions and Selfintersection Numbers 21
1.8 Reciprocity Law for Geometric Sums 28
1.9 Explicit Dedekind Sums 31
1.10 Eisenstein Sums 34
1.11 Hirzebruch s Sum 37
1.12 Geometric Interpretation 40
1.13 Quotients and Coverings of Modifications 46
1.14 Selfintersections of Quotient Curves 49
1.15 The Bridge Algorithm 53
1.16 First Orbital Properties 56
1.17 Local Orbital Euler Numbers 63
1.18 Absorptive Numbers 70
2 Orbital Curves 76
2.1 Point Arrangements on Curves 76
2.2 Euler Heights of Orbital Curves 78
2.3 The Geometric Local Global Principle 82
2.4 Signature Heights of Orbital Curves 85
3 Orbital Surfaces 94
3.1 Regular Arrangements on Surfaces 94
3.2 Basic Invariants and Fixed Point Theorem 98
3.3 Euler Heights 107
3.4 Signature Heights 115
3.5 Quasi homogeneous Points, Quotient Points and Cusp Points 124
3.6 Quasi smooth Orbital Surfaces 136
3.7 Open Orbital Surfaces 145
3.8 Orbital Decompositions 153
vi ^ Contents
4 Ball Quotient Surfaces 166
4.1 Ball Lattices 166
4.2 Neat Ball Cusp Lattices 170
4.3 Invariants of Neat Ball Quotient Surfaces 179
4.4 T Rational Discs 186
4.5 Cusp Singularities, Reflections and Elliptic Points 195
4.6 Orbital Ball Quotient Surfaces and Molecular 200
4.7 Invariants of Disc Quotient Curves 213
4.8 Invariants of Ball Quotient Surfaces . 219
4.9 Global Proportionality 231
4.10 Orbital Decompositions and the Finiteness
Theorem 233
4.11 Leading Examples 239
4.12 Towards the Count of Ball Metrics on Non Compact Surfaces . . 253
5 Picard Modular Surfaces 259
5.1 Classification Diagram 259
5.2 Picard Modular Surface of the Field of Eisenstein Numbers 261
5.3 Picard Modular Surface of the Field of Gauss Numbers . . 265
5.4 Kodaira Classification of Picard Modular Surfaces 274
5.5 Special Results and Examples 292
5AVolumes of Fundamental Domains of Picard Modular
Groups 300
5A.1 The Order of Finite Unitary Groups 301
5A.2 Index of Congruence Subgroups 308
5A.3 Local Volumina 316
5A.4 The Global Volume 321
6 Q Orbital Surfaces 330
6.1 Introduction 330
6.2 Arrangements with Rational Coefficients . 333
6.3 Finite Morphisms of Q Orbital Surfaces • 337
6.4 Functorial Properties for Rational Invariants 342
6.5 Euler and Signature Heights 347
6.6 Reduction of Galois Finite Morphisms 352
6.7 Local Base Changes 359
6.8 Global Base Changes 363
6.9 Explicit Hurwitz Formulas for Finite Surface Coverings . . 374
6.10 Finite Coverings of Ruled Surfaces and the Inequality
c? 2c2 390
Index 401
Bibliography 406
|
| any_adam_object | 1 |
| author | Holzapfel, Rolf-Peter 1942- |
| author_GND | (DE-588)117712817 |
| author_facet | Holzapfel, Rolf-Peter 1942- |
| author_role | aut |
| author_sort | Holzapfel, Rolf-Peter 1942- |
| author_variant | r p h rph |
| building | Verbundindex |
| bvnumber | BV011712008 |
| callnumber-first | Q - Science |
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:14:28Z |
| institution | BVB |
| isbn | 3528065117 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007898297 |
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| physical | XIII, 414 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Vieweg |
| record_format | marc |
| series2 | [Aspects of mathematics / E] |
| spelling | Holzapfel, Rolf-Peter 1942- Verfasser (DE-588)117712817 aut Ball and surface arithmetics Rolf-Peter Holzapfel Braunschweig ; Wiesbaden Vieweg 1998 XIII, 414 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier [Aspects of mathematics / E] 29 Surfaces algébriques ram Surfaces, Algebraic Kugel (DE-588)4165914-4 gnd rswk-swf Picard-Modulfläche (DE-588)4508898-6 gnd rswk-swf Komplexe algebraische Fläche (DE-588)4164889-4 gnd rswk-swf Kugelquotientenfläche (DE-588)4508897-4 gnd rswk-swf Arithmetik (DE-588)4002919-0 gnd rswk-swf Uniformisierung (DE-588)4268725-1 gnd rswk-swf Algebraische Fläche (DE-588)4195660-6 gnd rswk-swf Algebraische Fläche (DE-588)4195660-6 s Kugel (DE-588)4165914-4 s DE-604 Kugelquotientenfläche (DE-588)4508897-4 s Picard-Modulfläche (DE-588)4508898-6 s Komplexe algebraische Fläche (DE-588)4164889-4 s Uniformisierung (DE-588)4268725-1 s Arithmetik (DE-588)4002919-0 s E] [Aspects of mathematics 29 (DE-604)BV000018737 29 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007898297&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holzapfel, Rolf-Peter 1942- Ball and surface arithmetics Surfaces algébriques ram Surfaces, Algebraic Kugel (DE-588)4165914-4 gnd Picard-Modulfläche (DE-588)4508898-6 gnd Komplexe algebraische Fläche (DE-588)4164889-4 gnd Kugelquotientenfläche (DE-588)4508897-4 gnd Arithmetik (DE-588)4002919-0 gnd Uniformisierung (DE-588)4268725-1 gnd Algebraische Fläche (DE-588)4195660-6 gnd |
| subject_GND | (DE-588)4165914-4 (DE-588)4508898-6 (DE-588)4164889-4 (DE-588)4508897-4 (DE-588)4002919-0 (DE-588)4268725-1 (DE-588)4195660-6 |
| title | Ball and surface arithmetics |
| title_auth | Ball and surface arithmetics |
| title_exact_search | Ball and surface arithmetics |
| title_full | Ball and surface arithmetics Rolf-Peter Holzapfel |
| title_fullStr | Ball and surface arithmetics Rolf-Peter Holzapfel |
| title_full_unstemmed | Ball and surface arithmetics Rolf-Peter Holzapfel |
| title_short | Ball and surface arithmetics |
| title_sort | ball and surface arithmetics |
| topic | Surfaces algébriques ram Surfaces, Algebraic Kugel (DE-588)4165914-4 gnd Picard-Modulfläche (DE-588)4508898-6 gnd Komplexe algebraische Fläche (DE-588)4164889-4 gnd Kugelquotientenfläche (DE-588)4508897-4 gnd Arithmetik (DE-588)4002919-0 gnd Uniformisierung (DE-588)4268725-1 gnd Algebraische Fläche (DE-588)4195660-6 gnd |
| topic_facet | Surfaces algébriques Surfaces, Algebraic Kugel Picard-Modulfläche Komplexe algebraische Fläche Kugelquotientenfläche Arithmetik Uniformisierung Algebraische Fläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007898297&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT holzapfelrolfpeter ballandsurfacearithmetics |