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Riemannsche Flächen

Riemannsche Flächen

          
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About the Book

Dieses Buch ist aus Vorlesungen uber Riemannsche Flachen entstanden, die der Verfasser an den Universitaten Munchen, Regensburg und Munster gehalten hat. Das Ziel war, einer seits eine Einftihrung in dieses vie1faltige und schOne Gebiet zu geben und andrerseits Methoden der Theorie der kom plexen Mannigfaltigkeiten im Spezialfall der komplexen Dimension eins vorzustellen, wo sie besonders einfach und durchsichtig sind. Das Buch gliedert sich in drei Kapitel. 1m ersten Kapitel be trachten wir die Riemannschen Flachen vom Standpunkt der Uberlagerungstheorie aus und entwicke1n dazu in knapper Form die n6tigen topologischen Grundbegriffe. Es werden dann die Riemannschen Flachen konstruiert, die durch ana lytische Fortsetzung eines Funktionskeims entstehen, ins besondere auch die Riemannschen Flachen algebraischer Funktionen. AuBerdem beschaftigen wir uns genauer mit analytischen Funktionen, die ein spezielles Mehrdeutigkeits verhalten aufweisen, wie Stammfunktionen von holomor phen Differentialformen und L6sungen linearer Differential gleichungen. Das zweite Kapitel ist der Theorie der kompakten Riemann schen Flachen gewidmet. Es werden die klassischen Haupt satze behandelt, wie Satz von Riemann-Roch, Abelsches Theorem und lacobisches Umkehrproblem. Ein wichtiges technisches Hilfsmittel ist die Cohomologietheorie mit Werten in Garben. Wir beschranken uns dabei auf die Be trachtung der Cohomologiegruppen der Ordnung eins, die verhaltnismaBig e1ementar zu behande1n sind. Die Haupt- VI Vorwort satze folgen (nach Serre) alle aus der Endlich-Dimensionali tat der ersten Cohomologiegruppe mit Werten in der Garbe der holomorphen Funktionen. Der Beweis dieses Satzes wiederum beruht auf der lokalen Losbarkeit der inhomoge nen Cauchy-Riemannschen Gleichungen und auf dem Schwarzschen Lemma."


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Product Details
  • ISBN-13: 9783540080343
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Height: 203 mm
  • No of Pages: 226
  • Series Title: Heidelberger Taschenbücher
  • Weight: 254 gr
  • ISBN-10: 3540080341
  • Publisher Date: 01 Mar 1977
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Spine Width: 15 mm
  • Width: 135 mm


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