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Item Details
| Title:
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BALL AND SURFACE ARITHMETICS
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| By: |
Rolf-Peter Holzapfel |
| Format: |
Paperback |
| List price:
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£72.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
3322901718 |
| ISBN 13: |
9783322901712 |
| Publisher: |
SPRINGER FACHMEDIEN WIESBADEN |
| Pub. date: |
26 February, 1998 |
| Edition: |
Softcover reprint of the original 1st ed. 1998 |
| Series: |
Aspects of Mathematics 29 |
| Pages: |
414 |
| Language: |
English & German |
| Translated from: |
German |
| Synopsis: |
Bei hoherdimensionalen komplexen Mannigfaltigkeiten stellt die Riemann-Roch-Theorie die grundlegende Verbindung von analytischen bzw. algebraischen zu topologischen Eigenschaften her. Dieses Buch befasst sich mit Mannigfaltigkeiten der komplexen Dimension 2, d. h. mit komplexen Flachen. Hauptziel der Monographie ist es, neue rationale diskrete Invarianten (Hohen) in die Theorie komplexer Flachen explizit einzufuhren und ihre Anwendbarkeit auf konkrete aktuelle Probleme darzustellen.Als erste unmittelbare Anwendung erhalt man explizit und ganz allgemein Formeln vom Hurwitz-Typ endlicher Flachenuberlagerungen fur die vier klassischen Invarianten, die auf andere Weise bisher nur in Spezialfallen zuganglich waren. Ein weiteres Anwendungsgebiet ist die Theorie der Picardschen Modulflachen: Neue Resultate werden beschrieben. Letztendlich kann im letzten Kapitel eine Erganzung des bekannten Satzes von Bogomolov-Miyaoka-Yau mit Hilfe der Hohentheorie gezeigt werden. The monograph presents basically an arithmetic theory of orbital surfaces with cusp singularities. As main invariants orbital hights are introduced, not only for the surfaces but also for the components of orbital cycles.These invariants are rational numbers with nice functorial properties allowing precise formulas of Hurwitz type and a fine intersection theory for orbital cycles. For ball quotient surfaces they appear as volumes of fundamental domains. In the special case of Picard modular surfaces they are discovered by special value of Dirichlet L-series or higher Bernoulli numbers. As a central point of the monograph a general Proportionality Theorem in terms of orbital hights is proved. It yields a strong criterion to decide effectively whether a surface with given cycle supports a ball quotient structure being Kaehler-Einstein with negative constant holomorphic sectional curvature outside of this cycle. The theory is applied to the classification of Picard modular surfaces and to surfaces geography. |
| Illustrations: |
biography |
| Publication: |
Germany |
| Imprint: |
Vieweg+Teubner Verlag |
| Returns: |
Returnable |
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