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Symmetries Of Accola-Maclachlan And Kulkarni Surfaces

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Gamboa, J. M. and Broughton, SA and Bujalance, E. and Costa, F.A. and Gromadzki, G. (1999) Symmetries Of Accola-Maclachlan And Kulkarni Surfaces. Proceedings of the American Mathematical Society, 127 (3). pp. 637-646. ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/1999-127-03/S0002-9939-99-04534-7/S0002-9939-99-04534-7.pdf


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Abstract

For all g 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 suciently 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.


Item Type:Article
Uncontrolled Keywords:Orders Of Automorphism Groups Of Riemann Surfaces; Kulkarni Surface; Number Of Ovals; Symmetries; Real Forms Of Accola-Maclachlan Surfaces
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15339
Deposited On:24 May 2012 09:44
Last Modified:22 Aug 2018 10:21

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