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Über diejenigen algebraischen Gebilde, welche eindeutige Transformationen in sich zulassen

In: Mathematische Werke

Author

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  • Adolf Hurwitz

Abstract

Zusammenfassung In den nachfolgenden Zeilen beschäftige ich mich namentlich mit der Aufgabe: alle irreduzibeln algebraischen Gleichungen f = ( s , z ) = 0 $$f = (s,z) = 0$$ zu bestimmen, welche durch eine rationale eindeutig umkehrbare Transformation { s ′ = φ ( s , z ) z ′ = ψ ( s , z ) $$\left\{ \begin{gathered}s' = \varphi (s,z) \hfill \\z' = \psi (s,z) \hfill \\\end{gathered} \right.$$ in sich übergeführt werden können, oder — was offenbar auf dasselbe hinauskommt — alle diejenigen Riemann’schen Flächen (algebraischen Gebilde) anzugeben, auf welchen eine ein-eindeutige algebraische Korrespondenz (s, z; s′, z′) existiert. Der Fall, in welchem das Geschlecht p des Gebildes gleich Null oder Eins ist, bildet bei dieser Untersuchung einen leicht für sich zu behandelnden, übrigens seit langem erledigten Ausnahmefall. Ich setze deshalb im Folgenden, wenn ich nicht ausdrücklich das Gegenteil bemerke, stets voraus, dass das Geschlecht der zu betrachtenden Gebilde grösser ist als Eins.

Suggested Citation

  • Adolf Hurwitz, 1932. "Über diejenigen algebraischen Gebilde, welche eindeutige Transformationen in sich zulassen," Springer Books, in: Mathematische Werke, chapter 0, pages 241-259, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-4161-0_12
    DOI: 10.1007/978-3-0348-4161-0_12
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