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An analytic proof of Severi’s theorem. (English) Zbl 0585.32025
A classical theorem of Severi states that a fixed compact Riemann surface R may be mapped holomorphically onto only finitely many Riemann surfaces of genus greater than one. The pesent paper gives an analytic proof of a more general result. It is proved that: If R is a hyperbolic Riemann surface of finite conformal type then for at most finitely many hyperbolic surfaces S are there non-constant holomorphic mappings from R into S. The proof is a clever application of deformation-theoretic techniques.
Reviewer: W.Abikoff

32G15 Moduli of Riemann surfaces, Teichm├╝ller theory (complex-analytic aspects in several variables)
30F10 Compact Riemann surfaces and uniformization
14E05 Rational and birational maps
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