2026-06-28T15:00:36Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/573982024-07-11T13:04:02Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Bujalance García, Emilio
author
Gamboa Mutuberria, José Manuel
author
Martens, Gerriet
author
Etayo Gordejuela, José Javier
2023-06-20T16:54:36Z
2023-06-20T16:54:36Z
1989
Bujalance García, E., Gamboa Mutuberria, J. M., Martens, G. & Etayo Gordejuela, J. J. «Minimal Genus of Klein Surfaces Admitting an Automorphism of a given Order». Archiv Der Mathematik, vol. 52, n.o 2, febrero de 1989, pp. 191-202. DOI.org (Crossref), https://doi.org/10.1007/BF01191274.
0003-889X
10.1007/BF01191274
https://hdl.handle.net/20.500.14352/57398
https//doi.org/10.1007/BF01191274
http://www.springerlink.com/content/p60j7tu265313n66/
Let K be a compact Klein surface of algebraic genus $g\ge 2,$ which is not a classical Riemann surface. The authors show that if K admits an automorphism of order $N>2,$ then it must have algebraic genus at least $(p\sb 1-1)N/p\sb 1$ if N is prime or if its smallest prime factor, $p\sb 1$, occurs with exponent 1 in N. Otherwise the genus is at least $(p\sb 1-1)(N/p\sb 1-1)$. This result extends to bordered Klein surfaces a result of {\it E. Bujalance} [Pac. J. Math. 109, 279-289 (1983)] and is the analog for Klein surfaces of a result of {\it W. J. Harvey} [Q. J. Math., Oxf. II. Ser. 17, 86-97 (1966)] and, ultimately, of {\it A. Wiman} [Kongl. Svenska Vetenskaps-Akad. Handl., Stockholm 21, No.1 and No.3 (1895)].
Minimal genus of Klein surfaces admitting an automorphism of a given order
journal article