Large automorphism groups of hyperelliptic Klein surfaces



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Bujalance, E. and Etayo Gordejuela, J. Javier (1988) Large automorphism groups of hyperelliptic Klein surfaces. Proceedings of the American Mathematical Society, 103 (3). pp. 679-686. ISSN 0002-9939

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A bordered Klein surface of algebraic genus p has at most 12(p-1) automorphisms and this is attained for infinitely many values of p. Furthermore, for an infinity of values of p, the largest group of automorphisms of such a surface is $4(p+1)$ or 4p depending on whether the surface is orientable or not [{\it C. L. May}, Pac. J. Math. 59, 199- 210 (1975) and Proc. Am. Math. Soc. 63, 273-280 (1977]. \par Here the authors examine such surfaces which are additionally hyperelliptic and have automorphism groups of order exceeding 4(p-1). Using their characterization of hyperelliptic Klein surface via non- Euclidean crystallographic groups [Q. J. Math., Oxf. II. Ser. 36, 141-157 (1985)] the authors determine these automorphism groups, which are all dihedral or direct sums of a dihedral group and a cyclic group of order 2, and the corresponding topological type of the surface.

Item Type:Article
Uncontrolled Keywords:Fuchsian groups and their generalizations; Curves; Compact Riemann surfaces and uniformization
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15766
Deposited On:26 Jun 2012 10:47
Last Modified:07 Aug 2018 07:22

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