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W. V. D. Hodge, D. Pedoe's Methods of algebraic geometry PDF

By W. V. D. Hodge, D. Pedoe

ISBN-10: 0521467756

ISBN-13: 9780521467759

ISBN-10: 0521469015

ISBN-13: 9780521469012

ISBN-10: 0521469074

ISBN-13: 9780521469074

Within the 3rd quantity, the authors speak about algebraic types on a flooring box with out attribute, and care for extra complicated geometrical equipment, similar to valuation thought.

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CorolIar. Sei X eine einfach zusammenhangende Riemannsche Flache, aEX und

11. Defmition. Seien X, Y topologische Raume. , jeJ J ยง 4. Verzweigte und unverzweigte UberJagerungen 23 wobei die Vj,jEJ, paarweise disjunkte offene Teilmengen von Yund alle Abbildungen pi Vj --+ U Homoomorphismen sind. ) Bemerkung. In Lehrbtichern der Topologie versteht man unter einer Uberlagerung meist das, was wir hier als unverzweigte, unbegrenzte Uberlagerung bezeichnen. In der Funktionentheorie ist es jedoch wichtig, auch verzweigte und begrenzte Uberlagerungen zu betrachten. 12. Beispieie.

B) Wir zeigenjetzt, daB p: Iffl-Xlokal-topologisch ist. Sei qJElffl undp(qJ) = x. 40 Kapitel 1. B mit qJE[U,j]. Dann ist [U,j] offene Umgebung von qJ und U offene Umgebung von x. Die Abbildung pi [U,j]---+U ist bijektiv und, wie sofort aus den Definitionen folgt, stetig und offen. p: IjOl---+X ist also lokal-topologisch. 9. Defmition. (g) fUr einen Punkt aEY tibereinstimmen, so giltf=g. B. ) und vi{ der holomorphen bzw. meromorphen Funktionen auf einer Riemannschen Flache X erfUllt. 10. Satz. Sei X ein lokal zusammenhiingender Hausdorffraum und jO eine Priigarbe auf X, die dem Identitiitssatz geniigt.

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Methods of algebraic geometry by W. V. D. Hodge, D. Pedoe


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