Publication: Fuchsian groups generated by half-turns and geometrical characterization of hyperelliptic and symmetric Riemann surfaces
No Thumbnail Available
Official URL
Full text at PDC
Publication Date
2004
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Matematisk Institut, Universitetsparken NY Munkegade
Citations
Exportar
Abstract
We construct a special type of fundamental regions for any Fuchsian group $F$ generated, by an even number of half-turns, and for certain non-Euclidean crystallographic groups (NEC groups in short). By comparing these regions we give geometrical conditions for F to be the canonical Fuchsian subgroup of one of those NEC groups. Precisely speaking, we deal with NEC groups of algebraic genus 0 having all periods in the signature equal to 2. By means of these conditions we give a characterization of hyperelliptic and symmetric Riemann surfaces.
Description
UCM subjects
Unesco subjects
Keywords
Citation
Bujalance, E., Etayo, J. J., Characterization of q -Hyperelliptic compact planar Klein surfaces, Abh. Math. Sem. Univ. Hamburg 58 (1988), 95–104.
Bujalance, E., Etayo, J. J., Gamboa, J. M., Hyperelliptic Klein surfaces, Quart. J. Math. Oxford (2) 36 (1985), 141–157.
Bujalance, E., Etayo, J. J., Gamboa, J. M., Superficies de Klein elípticas hiperelípticas, Memorias de la Real Academia de Ciencias, Tomo XIX (1985).
Bujalance, E., Singerman, D., The symmetry type of a Riemann surface, Proc. London Math. Soc. (3) 51 (1985), 501–519.
Bujalance, J. A., Hyperelliptic compact non-orientable Klein surfaces without boundary, Kodai Math. J. 12 (1989), 1–8.
Maskit, B., A New Characterization of Hyperellipticity, Michigan Math. J. 47 (2000), 3–14.
Macbeath, A. M., The classification of non-euclidean crystallographic groups, Canad. J. Math. 19 (1967), 1192–1205.
Schmutz Schaller, P., Geometric characterization of hyperelliptic Riemann surfaces, Ann. Acad. Sci. Fenn. Math. 25 (2000), 85–90
Singerman, D., On the structure of non-euclidean crystallographic groups, Proc. Cambridge Philos. Soc. 76 (1974), 233–240.
Wilkie, H. C., On non-Euclidean crystallographic groups, Math. Z. 91 (1966), 87–102.
Wiman, A., Über die hyperelliptischen Kurven und diejenigen vom Geschlecht p=3 , welche eindeutigen Transformationen in sich zulassen, Bihang Till. Kongl. Svenska Vetenskaps-Akademiens Handlingar 21,1 n.1 (1895), 23 pp.