Introduction to Complex Hyperbolic Spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1987
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Since the appearance of Kobayashi's book, there have been several re sults at the basic level of hyperbolic spaces, for instance Brody's theorem, and results of Green, Kiernan, Kobayashi, Noguchi, etc. which make it worthwhile to have a systematic exposition. Although of necessity I re produce some theorems from Kobayashi, I take a different direction, with different applications in mind, so the present book does not super sede Kobayashi's. My interest in these matters stems from their relations with diophan tine geometry. Indeed, if X is a projective variety over the complex numbers, then I conjecture that X is hyperbolic if and only if X has only a finite number of rational points in every finitely generated field over the rational numbers. There are also a number of subsidiary conjectures related to this one. These conjectures are qualitative. Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures. Noguchi has looked at the function field case and made substantial progress, after the line started by Grauert and Grauert-Reckziegel and continued by a recent paper of Riebesehl. The book is divided into three main parts: the basic complex analytic theory, differential geometric aspects, and Nevanlinna theory. Several chapters of this book are logically independent of each other |
| Beschreibung: | 1 Online-Ressource (VIII, 272 p) |
| ISBN: | 9781475719451 9781441930828 |
| DOI: | 10.1007/978-1-4757-1945-1 |
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Datensatz im Suchindex
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| author | Lang, Serge |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| id | DE-604.BV042421297 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781475719451 9781441930828 |
| language | English |
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| spelling | Lang, Serge Verfasser aut Introduction to Complex Hyperbolic Spaces by Serge Lang New York, NY Springer New York 1987 1 Online-Ressource (VIII, 272 p) txt rdacontent c rdamedia cr rdacarrier Since the appearance of Kobayashi's book, there have been several re sults at the basic level of hyperbolic spaces, for instance Brody's theorem, and results of Green, Kiernan, Kobayashi, Noguchi, etc. which make it worthwhile to have a systematic exposition. Although of necessity I re produce some theorems from Kobayashi, I take a different direction, with different applications in mind, so the present book does not super sede Kobayashi's. My interest in these matters stems from their relations with diophan tine geometry. Indeed, if X is a projective variety over the complex numbers, then I conjecture that X is hyperbolic if and only if X has only a finite number of rational points in every finitely generated field over the rational numbers. There are also a number of subsidiary conjectures related to this one. These conjectures are qualitative. Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures. Noguchi has looked at the function field case and made substantial progress, after the line started by Grauert and Grauert-Reckziegel and continued by a recent paper of Riebesehl. The book is divided into three main parts: the basic complex analytic theory, differential geometric aspects, and Nevanlinna theory. Several chapters of this book are logically independent of each other Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Komplexer Raum (DE-588)4138419-2 gnd rswk-swf Hyperbolischer komplexer Raum (DE-588)4138418-0 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Hyperbolischer komplexer Raum (DE-588)4138418-0 s 1\p DE-604 Komplexer Raum (DE-588)4138419-2 s 2\p DE-604 Hyperbolische Geometrie (DE-588)4161041-6 s 3\p DE-604 Differentialgeometrie (DE-588)4012248-7 s 4\p DE-604 Mehrere komplexe Variable (DE-588)4169285-8 s 5\p DE-604 https://doi.org/10.1007/978-1-4757-1945-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lang, Serge Introduction to Complex Hyperbolic Spaces Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Komplexer Raum (DE-588)4138419-2 gnd Hyperbolischer komplexer Raum (DE-588)4138418-0 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4138419-2 (DE-588)4138418-0 (DE-588)4161041-6 (DE-588)4169285-8 |
| title | Introduction to Complex Hyperbolic Spaces |
| title_auth | Introduction to Complex Hyperbolic Spaces |
| title_exact_search | Introduction to Complex Hyperbolic Spaces |
| title_full | Introduction to Complex Hyperbolic Spaces by Serge Lang |
| title_fullStr | Introduction to Complex Hyperbolic Spaces by Serge Lang |
| title_full_unstemmed | Introduction to Complex Hyperbolic Spaces by Serge Lang |
| title_short | Introduction to Complex Hyperbolic Spaces |
| title_sort | introduction to complex hyperbolic spaces |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Komplexer Raum (DE-588)4138419-2 gnd Hyperbolischer komplexer Raum (DE-588)4138418-0 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Differentialgeometrie Komplexer Raum Hyperbolischer komplexer Raum Hyperbolische Geometrie Mehrere komplexe Variable |
| url | https://doi.org/10.1007/978-1-4757-1945-1 |
| work_keys_str_mv | AT langserge introductiontocomplexhyperbolicspaces |