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oai:docta.ucm.es:20.500.14352/572482024-02-29T19:22:36Zcom_20.500.14352_14col_20.500.14352_15

Double Coverings Of Klein Surfaces By A Given Riemann Surface Gamboa Mutuberria, José Manuel Bujalance, E. Conder, M.D.E Gromadzki, G. Izquierdo, Milagros 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. 2023-06-20T16:51:30Z 2023-06-20T16:51:30Z 2002 journal article 0022-4049 10.1016/S0022-4049(01)00082-2 https://hdl.handle.net/20.500.14352/57248 http://www.sciencedirect.com/science/article/pii/S0022404901000822 http://www.sciencedirect.com eng restricted access Elsevier Science