Download E-books Existenz semiuniverseller Deformationen in der komplexen Analysis (Aspects of Mathematics) (German Edition) PDF

By Harald Stieber

Jede komplexe Mannigfaltigkeit ist auf naturliche Weise eine differenzierbare !>1annigfaltigkeit. Sei umgekehrt M eine differenzierbare Mannigfaltigkeit. Es erhebt sich die Frage, ob auf M eine komplexe Struktur existiert. Falls dies der Fall ist, besteht dasnachste Problern darin, eine Ubersicht uber "alle" komplexen Strukturen auf M zu gewinnen. Sei L(M): =Menge der Aquivalenzklassen von komplexen Strukturen auf M Menge der zu M diffeornorphen, komplexen Mannigfalt- keiten/biholornorphe Aquivalenz. Das Modulproblern, das seinen Ursprung in der Arbeit [67] von B. Riernann hat, besteht darin, auf L(M) eine "naturliche" komplexe Struktur einzufuhren. Beispiel 1. Im Falle, dass M = ist, besteht L(M) aus zwei 1 Punkten, falls M = F ist, besteht L(M) nur aus einem Punkt (Riernannscher Abbildungssatz) . Beispiel 2. Sei w E mit Im w > zero und Gw: = {rnw+nlrn, nE }. Dann ist Tw: = /Gw ein Torus. Zwei Tori Tw' und T sind w genau dann biholornorph zueinander, wenn ganze Zahlen a, b, c, d mit advert - bc = 1 existieren, so dass + b w' = aw cw + d ist. Jeder Torus hat additionally einen Reprasentanten T mit w wEr: = {aE i Im Ct > zero, /Real:5. 2' Iai .:: . 1} . VIII Identifiziert guy entsprechende Punkte in r, so kann guy zeiaen. dass fur jeden Torus T gilt r(T) ""a: guy vergleiche dazu [39], instance 2.14. Beispiel three. Satz (Riemann, Teichmuller, Rauch, Ahlfors, Ber

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