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Analytische Stellenalgebren by O. Riemenschneider, Hans Grauert, Reinhold Remmert

Analytische Stellenalgebren

by O. Riemenschneider , Hans Grauert , Reinhold Remmert
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Book cover type: Paperback
  • ISBN13: 9783642650345
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 242
  • Original Price: EUR 60.74
  • Language: German
  • Edition: Softcover Repri
  • Item Weight: 345 grams
  • BISAC Subject(s): Mathematical Analysis

Indocti discant, et ament meminisse periti 1. Die Idee der Riemannschen Flache wird in der Funktionentheorie mehrerer komplexer Veranderlichen erst seit Beginn der 50er Jahre konsequent verwendet. Wie in der Funktionentheorie einer Verander- lichen muB man die Gebilde untersuchen, die durch groBtmogliche analytische Fortsetzung von holomorphen Funktionen entstehen. Die gleichen Griinde wie in der klassischen Funktionentheorie machen es notwendig, die Verzweigungspunkte hinzuzunehmen. Das fiihrte jedoch auf begriffiiche Schwierigkeiten, die 1933 H. Behnke und P. Thullen in ihrem Ergebnisbericht sogar veranlaBten, diese Punkte vorerst von der Betrachtung auszuschlieBen. Eine zufriedenstellende Definition des Ver- zweigungsbegriffs wurde erst 1951 von H. Behnke und K. Stein (Math. Ann. 124) gegeben. Die von ihnen eingefiihrten komplex n Riiume um- fassen insbesondere die analytischen Gebilde holomorpher Funktiollen mehrerer Veranderlicher, d. h. die hOherdimensionalen Riemannschen Flachen. Dabei stellte sich heraus, daB diese Riemannschen Gebilde - anders als in der klassischen Funktionentheorie - Punkte ohne lokale Uniformisierende besitzen konnen. Solche Punkte wurden fort an singu- lare Punkte genannt.

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