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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An explicit family of curves with trivial automorphism groups
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by Peter Turbek PDF
Proc. Amer. Math. Soc. 122 (1994), 657-664 Request permission


It is well known that a generic compact Riemann surface of genus greater than two admits only the identity automorphism; however, examples of such Riemann surfaces with their defining algebraic equations have not appeared in the literature. In this paper we give the defining equations of a doubly infinite, two-parameter family of projective curves (Riemann surfaces if defined over the complex numbers), whose members admit only the identity automorphism.
    W. L. Bailey, On the automorphism group of a generic curv e of genus greater than 2 , J. Math. Kyoto Univ. 1 (1961), 101-108. H. M. Farkras and I. Kra, Riemann surfaces, 2nd ed., Graduate Texts in Math., vol. 71, Springer-Verlag, Berlin and New York, 1991.
  • William Fulton, Algebraic curves. An introduction to algebraic geometry, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes written with the collaboration of Richard Weiss. MR 0313252
  • Leon Greenberg, Maximal Fuchsian groups, Bull. Amer. Math. Soc. 69 (1963), 569–573. MR 148620, DOI 10.1090/S0002-9904-1963-11001-0
  • Subhashis Nag, The complex analytic theory of Teichmüller spaces, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1988. A Wiley-Interscience Publication. MR 927291
  • Ivan Niven and Herbert S. Zuckerman, An introduction to the theory of numbers, 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0195783
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 122 (1994), 657-664
  • MSC: Primary 14H55
  • DOI:
  • MathSciNet review: 1242107