A transcendental view of the space of algebraic Riemann surfaces
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- Bull. Amer. Math. Soc. 71 (1965), 1-39
References
- Lars V. Ahlfors, On quasiconformal mappings, J. Analyse Math. 3 (1954), 1–58; correction, 207–208. MR 64875, DOI 10.1007/BF02803585
- Lars V. Ahlfors, The complex analytic structure of the space of closed Riemann surfaces. , Analytic functions, Princeton Univ. Press, Princeton, N.J., 1960, pp. 45–66. MR 0124486
- Lars V. Ahlfors, Some remarks on Teichmüller’s space of Riemann surfaces, Ann. of Math. (2) 74 (1961), 171–191. MR 204641, DOI 10.2307/1970309
- Lars V. Ahlfors, Curvature properties of Teichmüller’s space, J. Analyse Math. 9 (1961/62), 161–176. MR 136730, DOI 10.1007/BF02795342
- Lars V. Ahlfors, Teichmüller spaces, Proc. Internat. Congr. Mathematicians (Stockholm, 1962) Inst. Mittag-Leffler, Djursholm, 1963, pp. 3–9. MR 0176055
- Lars Ahlfors and Lipman Bers, Riemann’s mapping theorem for variable metrics, Ann. of Math. (2) 72 (1960), 385–404. MR 115006, DOI 10.2307/1970141
- Lars V. Ahlfors and Leo Sario, Riemann surfaces, Princeton Mathematical Series, No. 26, Princeton University Press, Princeton, N.J., 1960. MR 0114911, DOI 10.1515/9781400874538
- Aldo Andreotti, On a theorem of Torelli, Amer. J. Math. 80 (1958), 801–828. MR 102518, DOI 10.2307/2372835
- Walter L. Baily Jr., On the theory of $\theta$-functions, the moduli of abelian varieties, and the moduli of curves, Ann. of Math. (2) 75 (1962), 342–381. MR 162799, DOI 10.2307/1970178
- Lipman Bers, Spaces of Riemann surfaces, Proc. Internat. Congress Math. 1958., Cambridge Univ. Press, New York, 1960, pp. 349–361. MR 0124484
- Lipman Bers, Quasiconformal mappings and Teichmüller’s theorem, Analytic functions, Princeton Univ. Press, Princeton, N.J., 1960, pp. 89–119. MR 0114898
- Lipman Bers, Uniformization by Beltrami equations, Comm. Pure Appl. Math. 14 (1961), 215–228. MR 132175, DOI 10.1002/cpa.3160140304
- Lipman Bers, Holomorphic differentials as functions of moduli, Bull. Amer. Math. Soc. 67 (1961), 206–210. MR 122989, DOI 10.1090/S0002-9904-1961-10569-7
- Lipman Bers, Correction to “Spaces of Riemann surfaces as bounded domains”, Bull. Amer. Math. Soc. 67 (1961), 465–466. MR 130972, DOI 10.1090/S0002-9904-1961-10637-X
- Henri Cartan, Quotient d’un espace analytique par un groupe d’automorphismes, Algebraic geometry and topology. A symposium in honor of S. Lefschetz, Princeton University Press, Princeton, N.J., 1957, pp. 90–102 (French). MR 0084174 16. C. Chevalley and A. Weil, Über das Verhalten der Integrale 1. Gattung bei Automorphismen des Funktionenkörpers, Abh. Math. Sem. Univ. Hamburg 14 (1934), 358-361. 17. R. Fricke and F. Klein, Vorlesungen über die Theorie der Automorphen Funktionen, Teubner, Leipzig, 1926.
- Hans Grauert, Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen, Inst. Hautes Études Sci. Publ. Math. 5 (1960), 64 (German). MR 121814
- Leon Greenberg, Maximal Fuchsian groups, Bull. Amer. Math. Soc. 69 (1963), 569–573. MR 148620, DOI 10.1090/S0002-9904-1963-11001-0 20. A. Grothendieck, Techniques de construction en géometrie analytique, Séminaire H. Cartan 13 (1960/1961); Fascicules 1 and 2.
- Erich Hecke, Mathematische Werke, Vandenhoeck & Ruprecht, Göttingen, 1959 (German). Herausgegeben im Auftrage der Akademie der Wissenschaften zu Göttingen. MR 0104550 22. A. Hurwitz, Über diejenigen algebraischen Gebilde, welche eindeutige Transformationen in sich zulassen, Mathematische Werke, Bd. I, Birkhäuser, Basel, 1932, pp. 241-259; Über algebraische Gebilde mit eindeutigen Transformationen in sich, ibid, pp. 392-430.
- K. Kodaira and D. C. Spencer, Existence of complex structure on a differentiable family of deformations of compact complex manifolds, Ann. of Math. (2) 70 (1959), 145–166. MR 112158, DOI 10.2307/1969895 24. P. Koebe et al., Jber. Deutsch. Math.-Verein (1912).
- Saul Kravetz, On the geometry of Teichmüller spaces and the structure of their modular groups, Ann. Acad. Sci. Fenn. Ser. A I No. 278 (1959), 35. MR 0148906
- M. Kuranishi, On the locally complete families of complex analytic structures, Ann. of Math. (2) 75 (1962), 536–577. MR 141139, DOI 10.2307/1970211
- Joseph Lewittes, Invariant quadratic differentials, Bull. Amer. Math. Soc. 68 (1962), 320–322. MR 138757, DOI 10.1090/S0002-9904-1962-10788-5
- Joseph Lewittes, Gaps at Weierstrass points for the modular group, Bull. Amer. Math. Soc. 69 (1963), 578–582. MR 148621, DOI 10.1090/S0002-9904-1963-11006-X
- Joseph Lewittes, Automorphisms of compact Riemann surfaces, Amer. J. Math. 85 (1963), 734–752. MR 160893, DOI 10.2307/2373117
- Joseph Lewittes, Riemann surfaces and the theta function, Acta Math. 111 (1964), 37–61. MR 156964, DOI 10.1007/BF02391007 31. A. M. Macbeath, Fuchsian groups, Mimeographed Notes, Aberdeen.
- Henrik H. Martens, Torelli’s theorem and a generalization for hyper-elliptic surfaces, Comm. Pure Appl. Math. 16 (1963), 97–110. MR 152648, DOI 10.1002/cpa.3160160202
- Theodor Meis, Die minimale Blätterzahl der Konkretisierungen einer kompakten Riemannschen Fläche, Schr. Math. Inst. Univ. Münster 16 (1960), 61 (German). MR 147643
- David Mumford, An elementary theorem in geometric invariant theory, Bull. Amer. Math. Soc. 67 (1961), 483–487. MR 150148, DOI 10.1090/S0002-9904-1961-10647-2
- Rolf Nevanlinna, Uniformisierung, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band LXIV, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1953 (German). MR 0057335, DOI 10.1007/978-3-642-52801-9
- Emmy Noether, Der Endlichkeitssatz der Invarianten endlicher Gruppen, Math. Ann. 77 (1915), no. 1, 89–92 (German). MR 1511848, DOI 10.1007/BF01456821
- D. G. Northcott, Ideal theory, Cambridge Tracts in Mathematics and Mathematical Physics, No. 42, Cambridge, at the University Press, 1953. MR 0058575, DOI 10.1017/CBO9780511565908
- Charles Patt, Variations of Teichmueller and Torelli surfaces, J. Analyse Math. 11 (1963), 221–247. MR 160894, DOI 10.1007/BF02789986
- Albert Pfluger, Theorie der Riemannschen Flächen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0084031, DOI 10.1007/978-3-642-94698-1 40. E. Picard, Traite d’analyse, Vol. 2, Gauthier-Villars, Paris, 1893.
- H. E. Rauch, On the transcendental moduli of algebraic Riemann surfaces, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 42–49. MR 72232, DOI 10.1073/pnas.41.1.42
- H. E. Rauch, On the moduli of Riemann surfaces, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 236–238; errata, 421. MR 72234, DOI 10.1073/pnas.41.6.421
- H. E. Rauch, Weierstrass points, branch points, and moduli of Riemann surfaces, Comm. Pure Appl. Math. 12 (1959), 543–560. MR 110798, DOI 10.1002/cpa.3160120310
- H. E. Rauch, Variational methods in the problem of the moduli of Riemann surfaces. , Contributions to function theory (Internat. Colloq. Function Theory, Bombay, 1960) Tata Institute of Fundamental Research, Bombay, 1960, pp. 17–40. MR 0132173
- H. E. Rauch, The singularities of the modulus space, Bull. Amer. Math. Soc. 68 (1962), 390–394. MR 141781, DOI 10.1090/S0002-9904-1962-10818-0
- Bernhard Riemann, Gesammelte mathematische Werke und wissenschaftlicher Nachlass, Dover Publications, Inc., New York, N.Y., 1953 (German). MR 0052364 47. B. Riemann, Vorlesungen über die allgemeine Theorie der Integrale algebraischer Differentialen, ibid. Supplement I.
- Helmut Röhrl, On holomorphic families of fiber bundles over the Riemannian sphere, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 33 (1960/61), 435–477. MR 131881, DOI 10.1215/kjm/1250711997
- Menahem Schiffer and Donald C. Spencer, Functionals of finite Riemann surfaces, Princeton University Press, Princeton, N. J., 1954. MR 0065652
- F. Schottky, Über die Moduln der Thetafunctionen, Acta Math. 27 (1903), no. 1, 235–288 (German). MR 1554985, DOI 10.1007/BF02421309 51. G. Shimura, Modules des variétés abéliennes polarisiés et functions modulaires. I, II, III, Séminaire H. Cartan 10 (1957/1958); Volume 2.
- George Springer, Introduction to Riemann surfaces, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1957. MR 0092855
- Oswald Teichmüller, Extremale quasikonforme Abbildungen und quadratische Differentiale, Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1939 (1940), no. 22, 197 (German). MR 0003242
- Oswald Teichmüller, Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen, Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1943 (1943), no. 4, 42 (German). MR 0017803
- André Weil, Zum Beweis des Torellischen Satzes, Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. IIa. 1957 (1957), 33–53 (German). MR 0089483
- André Weil, Modules des surfaces de Riemann, Séminaire Bourbaki; 10e année: 1957/1958. Textes des conférences; Exposés 152 à 168; 2e éd. corrigée, Exposé 168, Secrétariat mathématique, Paris, 1958, pp. 7 (French). MR 0124485
- Hermann Weyl, Die Idee der Riemannschen Fläche, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1955 (German). 3te Aufl. MR 0069903
- A. L. Mayer, Special divisors and the Jacobian variety, Math. Ann. 153 (1964), 163–167. MR 164969, DOI 10.1007/BF01360314
Additional Information
- Journal: Bull. Amer. Math. Soc. 71 (1965), 1-39
- DOI: https://doi.org/10.1090/S0002-9904-1965-11225-3
- MathSciNet review: 0213543