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Proceedings of the American Mathematical Society

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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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Symmetries of Accola-Maclachlan and Kulkarni surfaces
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by S. A. Broughton, E. Bujalance, A. F. Costa, J. M. Gamboa and G. Gromadzki PDF
Proc. Amer. Math. Soc. 127 (1999), 637-646 Request permission

Abstract:

For all $g \ge 2$ there is a Riemann surface of genus $g$ whose automorphism group has order $8g+8$, establishing a lower bound for the possible orders of automorphism groups of Riemann surfaces. Accola and Maclachlan established the existence of such surfaces; we shall call them Accola-Maclachlan surfaces. Later Kulkarni proved that for sufficiently large $g$ the Accola-Maclachlan surface was unique for $g= 0,1,2\mod 4$ and produced exactly one additional surface (the Kulkarni surface) for $g= 3\mod 4$. In this paper we determine the symmetries of these special surfaces, computing the number of ovals and the separability of the symmetries. The results are then applied to classify the real forms of these complex algebraic curves. Explicit equations of these real forms of Accola-Maclachlan surfaces are given in all but one case.
References
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Additional Information
  • S. A. Broughton
  • Affiliation: Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803
  • MR Author ID: 42020
  • Email: allen.broughton@rose-hulman.edu
  • E. Bujalance
  • Affiliation: Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803
  • MR Author ID: 43085
  • Email: eb@mat.uned.es
  • A. F. Costa
  • Affiliation: Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803
  • MR Author ID: 51935
  • ORCID: 0000-0002-9905-0264
  • Email: acosta@mat.uned.es
  • J. M. Gamboa
  • Affiliation: Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803
  • Email: jmgamboa@eucmax.sim.ucm.es
  • G. Gromadzki
  • Affiliation: Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, Indiana 47803
  • Email: greggrom@mat.uned.es
  • Received by editor(s): November 15, 1995
  • Received by editor(s) in revised form: June 5, 1997
  • Additional Notes: The second and third authors were partially supported by DGICYT PB 95-0017 and CEE-CHRX-CT93-0408.
    The fourth author was partially supported by DGICYT PB 95-0354 and CEE-CHRX-CT93-0408
    The fifth author was partially supported by the Pedagogical University of Bydgoszcz.
  • Communicated by: Albert Baernstein II
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 637-646
  • MSC (1991): Primary 14H45, 14E09, 14H30
  • DOI: https://doi.org/10.1090/S0002-9939-99-04534-7
  • MathSciNet review: 1468184