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On Analytic Families of Compact Riemann Surfaces with Non-Trivial Automorphisms

Published online by Cambridge University Press:  22 January 2016

Akikazu Kuribayashi
Akikazu Kuribayashi*
Affiliation:
Chuo University
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The purpose of this paper is to investigate the moduli of compact Riemann surfaces with non-trivial automorphisms.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 28 , October 1966 , pp. 119 - 165
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Ahlfors, L. V., On quasiconformal mappings. J. Anal. Math., 3, 1–58 (1953–4).Google Scholar
[2] Ahlfors, L. V., The complex analytic structure of the space of closed Riemann surfaces. Analytic functions, Princeton Univ. Press., 1960, 45–60.Google Scholar
[3] Bers, L., Spaces of Riemann surfaces, Proc. Intern. Congr. Edinburgh, 1958.Google Scholar
[4] Bers, L., Quasiconformal Mappings and Teichmüller’s Theorem. Analytic functions. Princeton Univ. Press., 89–119.Google Scholar
[5] Bers, L., Spaces of Riemann surfaces as bounded domains, Bull. Amer. Math. Soc., vol. 66 (1960), 98–103.Google Scholar
[6] Bers, L., Holomorphic differentials as functions of moduli, Bull. Amer. Math. Soc., vol. 67 (1961), 206–210.Google Scholar
[7] Eichler, M., Einfuhlung in die Thorie der algebraischen Zahlen und Funktionen, Birkhäuser Verlag., 1963.Google Scholar
[8] Eichler, M., Eine Verallgemeinerung der Abelschen Integral. Math. Zeits. Bd., 67 (1957), 267–298.Google Scholar
[9] Hurwitz, A., Maht. Werke, Bd. I, Birkhäuser, Basel, 241–259, 321–390, 391–430.Google Scholar
[10] Igusa, J., Fiber systems of Jacobian varieties, Amer. J., of Math., 1956, 171–199.Google Scholar
[11] Koizumi, S. and Shimura, G., On specializations of abelian varieties, Scientific Papers of the College of General Education, Univ. of Tokyo, 9 (1959), 187–211.Google Scholar
[12] Lewittes, J., Automorphisms of compact Riemann surfaces, Amer. J. of Math., (1963), 738–752.Google Scholar
[13] Lewittes, J., Invariant quadratic differentials, Bull. Amer. Math. Soc., 68 (1962), 320–322.Google Scholar
[14] Mangler, W., Die Klassen von topologischen Abbildungen einer geschlossenen Fläche auf sich, Math. Zeits. Bd 44 (1939), 513–554.Google Scholar
[15] Séminaire, H. Cartan, E. N. S., 1953–54, Théorie des fonctions de plusieurs variables.Google Scholar
[16] Shimura, G., On analytic families of polarized abelian varieties and automorphic functions, Ann. of Math., 78 (1963), 149–192.Google Scholar
[17] Shimura, G. On purely transcendental fields of automorphic functions of several variables, Osaka J. Math. I (1964), 1–14.Google Scholar
[18] Shimura, G., Moduli and fibre systems of abelian varieties. To appear.Google Scholar
[19] Teichmüller, O., Extremale quasikonforme Abbildungen und quadratische differentiale, Preuss-Akad. Math.-naturw. kl., 22, 1940.Google Scholar
[20] Tuji, R., On conformal mapping of a hyperelliptic Riemann surfaces onto itself, Ködai Math. Sem. Rep., (1958), 127–136.Google Scholar
[21] Weil, A., Modules des surfaces de Riemann, Sem. Bourbaki May (1958).Google Scholar