### Impacto

Gamboa Mutuberria, José Manuel and Bujalance, E. and Etayo Gordejuela, J. Javier
(1986)
*Automorphism-Groups Of Real Algebraic-Curves Of Genus-3.*
Proceedings of the Japan Academy Series A-Mathematical Sciences, 62
(1).
pp. 40-42.
ISSN 0386-2194

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Official URL: http://projecteuclid.org/euclid.pja/1195514498

## Abstract

Let C be an algebraic curve of genus 3, defined over the real field R. The automorphism group of C is studied in this paper. In a paper by the same authors [Mich. Math.

J. 33, 55-74 (1986; see 20043 below)], the hyperelliptic case was solved, the authors found 5 abstract groups in that case. In the paper under review, a full classification

is announced, in which 8 abstract groups appear. A sketch of one of the new cases is given, full proofs appeared in Mem. R. Acad. Cienc. Exactas Fis. Nat. Madrid, Ser. Cienc. Exactas 19 (1985; see the following review)].

Item Type: | Article |
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Uncontrolled Keywords: | automorphism groups of real algebraic curves; Klein surfaces |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 15378 |

References: | Alling, N. L. and Greenleaf, N.: Foundations of the theory of Klein surfaces. Lect. Notes in Math., vol. 219, Springer (1971). Bujalance, E., Etayo, J. J., and Gamboa, J.M.: Superficies de Klein elipticashiperelipticas. Mem. R. Acad. Ci. (to appear). Groups of automorphism of hyperelliptic Klein surfaces of genus three. Michigan Math. J., vol. 33 (1986). Bujalance, E. Gamboa, J. M.: Automorphism groups of algebraic curves of R of genus two. Arch. Math., 42, 229-237 (1984). Coxeter, H. S. M. and Moser, W. O.J.: Generators and relations for discrete groups. Ergeb. der Math., vol. 14, Springer (4tl ed., 1980). Macbeath, A. M.: The classification of non-Euclidean plane crystallographic groups. Canad. J. Math., 19, 1192-1205 (1967). May, C. L.: Automorphisms of compact Klein surfaces with boundary. Pacific J. Math., $9, 199-210 (1975). Preston, R." Projective structures and fundamental domains on compact Klein surfaces. Ph. D. thesis, Univ. of Texas (1975). |

Deposited On: | 28 May 2012 08:41 |

Last Modified: | 06 Feb 2014 10:23 |

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