On the number of ovals of a symmetry of a compact Riemann surface
| dc.contributor.author | Gamboa Mutuberria, José Manuel | |
| dc.contributor.author | Bujalance, E. | |
| dc.contributor.author | Cirre, Francisco | |
| dc.contributor.author | Gromadzki, G. | |
| dc.date.accessioned | 2023-06-20T09:35:01Z | |
| dc.date.available | 2023-06-20T09:35:01Z | |
| dc.date.issued | 2008 | |
| dc.description.abstract | The set of stationary points of the anticonformal involution (reflection) of a Riemann surface is called an oval. In this paper the total number of ovals of all reflections on a surface is counted provided the group of conformal automorphisms of the surface is cyclic. The bounds for this number are also given. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Spanish Ministry of Education and Sciences[SAB2005-0049]; [MTM2005-01637]; [MTM2005-20865] | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15393 | |
| dc.identifier.doi | 10.4171/RMI/540 | |
| dc.identifier.issn | 0213-2230 | |
| dc.identifier.officialurl | http://projecteuclid.org/euclid.rmi/1218475347 | |
| dc.identifier.relatedurl | http://projecteuclid.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49963 | |
| dc.issue.number | 2 | |
| dc.journal.title | Revista Matemática Iberoamericana | |
| dc.page.final | 405 | |
| dc.page.initial | 391 | |
| dc.publisher | Universidad Autónoma Madrid | |
| dc.relation.projectID | E. Bujalance is partially supported by MTM2005-01637. F. J. Cirre is partially supported by MTM2005-01637. J. M. Gamboa | |
| dc.rights.accessRights | metadata only access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Riemann surface | |
| dc.subject.keyword | symmetries | |
| dc.subject.keyword | ovals | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | On the number of ovals of a symmetry of a compact Riemann surface | |
| dc.type | journal article | |
| dc.volume.number | 24 | |
| dcterms.references | Bujalance, E. and Conder, M. D. E.: On cyclic groups of automorphisms of Riemann surfaces. J. London Math. Soc. (2) 59 (1999), no. 2, 573–584. Bujalance, E., Costa, A. F. and Singerman, D.: Application of Hoare’s theorem to symmetries of Riemann surfaces. Ann. Acad. Sci. Fenn. Ser. A I Math. 18 (1993), no. 2, 307–322. Bujalance, E., Etayo, J. J., Gamboa, J. M. and Gromadzki, G.: Automorphism Groups of Compact Bordered Klein Surfaces. Lecture Notes in Math. 1439. Springer-Verlag, Berlin, 1990. Gromadzki, G.: On a Harnack-Natanzon theorem for the family of real forms of Riemann surfaces. J. Purc Appl. Algebra 121 (1997), no. 3, 253–269. Gromadzki, G.: On ovals on Riemann surfaces. Rev. Mat. Iberoamericana 16 (2000), no. 3, 515–527. Harnack, A.: U¨ ber die Vieltheiligkeit der ebenen algebraischen Kurven. Math. Ann. 10 (1876), 189–198. Klein, F.: U¨ ber Realita¨tsverha¨ltnisse bei der einem beliebigen Geschlechte zugeho¨rigen Normalkurve der '. Math. Ann. 42 (1893), no. 1, 1–29. Izquierdo, M. and Singerman, D.: Pairs of symmetries of Riemann surfaces. Ann. Acad. Sci. Fenn. Math. 23 (1998), no. 1, 3–24. Meleko˘glu, A.: Symmetries of Riemann Surfaces and Regular Maps. Doctoral thesis, Faculty of Mathematical Studies, University of Southampton, 1998. Nakamura, G.: The existence of symmetric Riemann surfaces determined by cyclic groups. Nagoya Math. J. 151 (1998), 129–143. Natanzon, S. M.: Finite groups of homeomorphisms of surfaces, and real forms of complex algebraic curves. (Russian). Trudy Moskov. Mat. Obshch. 51 (1988), 3–53, 258. Translation in Trans. Moscow Math. Soc. (1989), 1–51. Natanzon, S. M.: On the total number of ovals of real forms of complex algebraic curves. Uspekhi Mat. Nauk (1) 35, 1980, 207–208. (Russian Math. Surveys (1) 35, 1980, 223–224. Singerman, D.: On the structure of non-euclidean crystallographic groups. Proc. Cambridge Philos. Soc. 76 (1974), 233–240. Singerman, D.: Mirrors on Riemann surfaces. In Second International Conference on Algebra (Barnaul, 1991), 411–417. Contemp. Math. 184. Amer. Math. Soc., Providence, RI, 1995. Weichold, G.: U¨ ber symmetrische Riemannsche Fla¨chen und die Periodizita¨tsmodulen der zugerh¨origen Abelschen Normalintegrale erstes Gattung. Dissertation, Leipzig, 1883. | |
| dspace.entity.type | Publication | |
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