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Generalizations of de Franchis theorem. (English) Zbl 0517.32010

MSC:
32H99 Holomorphic mappings and correspondences
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
14H45 Special algebraic curves and curves of low genus
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[1] A. Borel and R. Narasimhan, Uniqueness conditions for certain holomorphic mappings , Invent. Math. 2 (1967), 247-255. · Zbl 0145.31802 · doi:10.1007/BF01425403 · eudml:141856
[2] M. de Franchis, Un teorema sulle involuzioni irrationali , Rend. Circ. Mat. Palermo 36 (1913), 368. · JFM 44.0657.02
[3] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II , Ann. of Math. (2) 79 (1964), 109-203; ibid. (2) 79 (1964), 205-326. JSTOR: · Zbl 0122.38603 · doi:10.2307/1970486 · links.jstor.org
[4] P. A. Griffiths, Complex-analytic properties of certain Zariski open sets on algebraic varieties , Ann. of Math. (2) 94 (1971), 21-51. JSTOR: · Zbl 0221.14008 · doi:10.2307/1970733 · links.jstor.org
[5] Y. Imayoshi, Holomorphic families of Riemann surfaces and Teichmüller spaces , Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 277-300. · Zbl 0476.32025
[6] Y. Imayoshi, Holomorphic families of Riemann surfaces and Teichmüller spaces. II , Tôhoku Math. J. (2) 31 (1979), no. 4, 469-489. · Zbl 0472.30038 · doi:10.2748/tmj/1178229731
[7] Y. Imayoshi, Holomorphic families of Riemann surfaces and Teichmüller spaces. III. Bimeromorphic embedding of algebraic surfaces into projective spaces by automorphic forms , Tôhoku Math. J. (2) 33 (1981), no. 2, 227-247. · Zbl 0504.32019 · doi:10.2748/tmj/1178229451
[8] A. Kas, On deformations of a certain type of irregular algebraic surface , Amer. J. Math. 90 (1968), 789-804. JSTOR: · Zbl 0202.51702 · doi:10.2307/2373484 · links.jstor.org
[9] S. Kobayashi, Hyperbolic manifolds and holomorphic mappings , Pure and Applied Mathematics, vol. 2, Marcel Dekker Inc., New York, 1970. · Zbl 0207.37902
[10] S. Kobayashi and T. Ochiai, Meromorphic mappings onto compact complex spaces of general type , Invent. Math. 31 (1975), no. 1, 7-16. · Zbl 0331.32020 · doi:10.1007/BF01389863 · eudml:142353
[11] S. Lang, Diophantine geometry , Interscience Tracts in Pure and Applied Mathematics, No. 11, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. · Zbl 0115.38701
[12] H. H. Martens, Remarks on de Franchis’ Theorem , (to appear). · Zbl 0527.14025
[13] T. Nishino, Prolongements analytiques au sens de Riemann , Bull. Soc. Math. France 107 (1979), no. 1, 97-112. · Zbl 0414.30033 · numdam:BSMF_1979__107__97_0 · eudml:87363
[14] J. Noguchi and T. Sunada, Finiteness of the family of rational and meromorphic mappings into algebraic varieties , Amer. J. Math. 104 (1982), no. 4, 887-900. JSTOR: · Zbl 0502.14002 · doi:10.2307/2374210 · links.jstor.org
[15] Ch. Pommerenke, Polymorphic functions for groups of divergence type , Math. Ann. 258 (1981/82), no. 4, 353-366. · Zbl 0489.30036 · doi:10.1007/BF01453971 · eudml:163603
[16] P. Samuel, Lectures on old and new results on algebraic curves , Notes by S. Anantharaman. Tata Institute of Fundamental Research Lectures on Mathematics, No. 36, Tata Institute of Fundamental Research, Bombay, 1966. · Zbl 0165.24102
[17] F. Severi, Trattato di Geometria Algebrica , vol. I, Nicola Zanichelli, Bologna, 1926, parte I. · JFM 52.0650.01
[18] H. Shimizu, On discontinuous groups operating on the product of the upper half planes , Ann. of Math. (2) 77 (1963), 33-71. JSTOR: · Zbl 0218.10045 · doi:10.2307/1970201 · links.jstor.org
[19] T. Sunada, Holomorphic mappings into a compact quotient of symmetric bounded domain , Nagoya Math. J. 64 (1976), 159-175. · Zbl 0352.32030
[20] T. Sunada, Rigidity of certain harmonic mappings , Invent. Math. 51 (1979), no. 3, 297-307. · Zbl 0418.31005 · doi:10.1007/BF01389922 · eudml:142638
[21] M. Tsuji, Potential theory in modern function theory , Chelsea Publishing Co., New York, 1975. · Zbl 0322.30001
[22] T. Urata, Holomorphic mappings onto a certain compact complex analytic space , Tôhoku Math. J. (2) 33 (1981), no. 4, 573-585. · Zbl 0477.32025 · doi:10.2748/tmj/1178229357
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