Double Coverings Of Klein Surfaces By A Given
Riemann Surface
| dc.contributor.author | Gamboa Mutuberria, José Manuel | |
| dc.contributor.author | Bujalance, E. | |
| dc.contributor.author | Conder, M.D.E | |
| dc.contributor.author | Gromadzki, G. | |
| dc.contributor.author | Izquierdo, Milagros | |
| dc.date.accessioned | 2023-06-20T16:51:30Z | |
| dc.date.available | 2023-06-20T16:51:30Z | |
| dc.date.issued | 2002 | |
| dc.description.abstract | Let X be a Riemann surface. Two coverings p1 : X → Y1 and p2 : X → Y2 are said to be equivalent if p2 =’p1 for some conformal homeomorphism ’: Y1 → Y2. In this paper we determine, for each integer g¿2, the maximum number R(g) of inequivalent rami>ed coverings between compact Riemann surfaces X → Y of degree 2; where X has genus g. Moreover, for in>nitely many values of g, we compute the maximum number U(g) of inequivalent unrami>ed coverings X → Y of degree 2 where X has genus g and admits no rami>ed covering. For the remaining values of g, the computation of U(g) relies on a likely conjecture on the number of conjugacy classes of 2-groups. We also extend these results to double coverings X → Y , where. Y is now a proper Klein surface. In the language of algebraic geometry, this means we calculate the number of real forms admitted by the complex algebraic curve X . c 2002 Elsevier Science B.V. All rights reserved. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGICYT PB 95-0017;N.Z. Marsden Fund;DGICYT PB98-0756; | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15276 | |
| dc.identifier.doi | 10.1016/S0022-4049(01)00082-2 | |
| dc.identifier.issn | 0022-4049 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0022404901000822 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57248 | |
| dc.issue.number | 2-3 | |
| dc.journal.title | Journal Of Pure And Applied Algebra | |
| dc.language.iso | eng | |
| dc.page.final | 151 | |
| dc.page.initial | 137 | |
| dc.publisher | Elsevier Science | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.986 | |
| dc.subject.keyword | Degree 2 Coverings | |
| dc.subject.keyword | Real Forms Of Algebraic Curves | |
| dc.subject.ucm | Álgebra | |
| dc.subject.unesco | 1201 Álgebra | |
| dc.title | Double Coverings Of Klein Surfaces By A Given Riemann Surface | |
| dc.type | journal article | |
| dc.volume.number | 169 | |
| dcterms.references | D.M. Accola, On lifting the hyperelliptic involution, Proc. Amer. Math. Soc. 122 (1994) 341–347. N.L. Alling, N. Greenleaf, Foundations of the Theory of Klein Surfaces, Lecture Notes in Mathematics, Vol. 219, Springer, Berlin, 1971. W. Bosma, J. Cannon, Handbook of Magma Functions, University of Sydney, Sydney, 1994. E. Bujalance et al. / Journal of Pure and Applied Algebra 169 (2002) 137–151 151 E. Bujalance, A classi>cation of unrami>ed double coverings of hyperelliptic Riemann surfaces, Arch. Math. 47 (1986) 93–96. E. Bujalance, F.J. Cirre, J.M. Gamboa, G. Gromadzki, Symmetry types of hyperelliptic Riemann surfaces, Memo. Soc. Math. France, to appear. E. Bujalance, G. Gromadzki, On rami>ed double covering maps of Riemann surfaces, J. Pure Appl. Algebra 146 (2000) 29–34. E. Bujalance, G. Gromadzki, M. Izquierdo, On real forms of a complex algebraic curve, J. Austral. Math. Soc. Ser. A 69 (2000) 1–9. F.J. Cirre, Complex automorphism groups of real algebraicc urves of genus 2, J. Pure Appl. Algebra 157 (2–3) (2001) F.J. Cirre, J.M. Gamboa, Klein surfaces and real algebraic curves, Proceedings of the Conference on Riemann surfaces, Madrid, 1998, Lecture Notes of the London Mathematical Society, Vol. 287, Cambridge Univ. Press, Cambridge, 2001, pp. 113–131. A. Duma, Zur Konkretisierung Kompakter Riemannscher FlQachen, Bayer Akad. Wiss. Math-Natur II (1974) 87–100. H.M. Farkas, Unrami>ed double coverings of hyperelliptic H.M. Farkas, Unrami>ed double coverings of hyperelliptic surfaces II, Proc. Amer. Math. Soc. 101 (3) (1987) 470 – 474. H.M. Farkas, Unrami>ed coverings of hyperelliptic Riemann surfaces, in: Complex Analysis I, Lecture Notes in Mathematics, Vol. 1275, Springer, Berlin, 1987, pp. 113–130. G. Gromadzki, Symmetries of Riemann surfaces from a combinatorial point of view, Proceedings of the Conference on Riemann surfaces, Madrid, 1998, Lecture Notes of the London Math. Soc., Vol. 287, Cambridge Univ. Press, Cambridge, 2001. R. Horiuchi, Normal coverings of hyperelliptic Riemann surfaces, J. Math. Kyoto Univ. 19 (3) (1979) 497–523. T. Kato, On the realization problem of compact Riemann surfaces, Hokkaido Math. J. 10 (1981) 336 –347. A.M. Macbeath, Discontinous groups and birational transformations, Proceedings of Dundee Summer School, University of St. Andrews, St. Andrews, 1961. C. Maclachlan, Smooth coverings of hyperelliptic surfaces, Quart. J. Math. Oxford Ser. 2 22 (1971) 117–123. A.D. Mednykh, Hurwitz problem on the number of nonequivalent coverings of compact Riemann surfaces, Siber. Math. J. 23 (3) (1983) 415– 420. A.D. Mednykh, Nonequivalent coverings of Riemann surfaces with a prescribed rami>cation type, Siber. Math. J. 25 (4) (1984) 606 – 625. A.D. Mednykh, G.G. Pozdnyakova, Number of nonequivalent coverings of compact Riemann surfaces over a non-orientable compact surface, Siber. Math. J. 27 (1) (1986) 99–106. Th. Meis, Die minimale BlQatlerzahl der Konkretisierungen einer kompakten Riemannscher FlaQache, Schr. Math. Inst. Univ. MQunster, Vol. 16, 1960. P. Turbek, A necessary and suOcient condition for lifting the hyperelliptic involution, Proc. Amer. Math. Soc. 125 (9) (1997) 2615–2625. P. Turbek, The full automorphism group of the Kulkarni surface, Rev. Mat. Univ. Complut. Madrid 10 (2) (1997) 265–276. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 8fcb811a-8d76-49a2-af34-85951d7f3fa5 | |
| relation.isAuthorOfPublication.latestForDiscovery | 8fcb811a-8d76-49a2-af34-85951d7f3fa5 |
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