- journal article metadata
European Mathematical Society Publishing House
2017-03-24 14:03:38
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
33
2017
1
The double of the doubles of Klein surfaces
Antonio
Costa
Facultad de Ciencias, UNED, MADRID, SPAIN
Paola
Cristofori
Università di Modena e Reggio Emilia, MODENA, ITALY
Ana
Porto
Facultad de Ciencias, UNED, MADRID, SPAIN
Klein surface, Riemann surface, automorphism, real algebraic curve, moduli space
A Klein surface is a surface with a dianalytic structure. A double of a Klein surface $X$ is a Klein surface $Y$ such that there is a degree two morphism (of Klein surfaces) $Y \to X$. There are many doubles of a given Klein surface and among them the so-called natural doubles which are: the complex double, the Schottky double and the orienting double. We prove that if $X$ is a non-orientable Klein surface with non-empty boundary, the three natural doubles, although distinct Klein surfaces, share a common double: “the double of doubles” denoted by $DX$. We describe how to use the double of doubles in the study of both moduli spaces and automorphisms of Klein surfaces. Furthermore, we show that the morphism from $DX$ to $X$ is not given by the action of an isometry group on classical surfaces.
Functions of a complex variable
Algebraic geometry
183
194
10.4171/RMI/932
http://www.ems-ph.org/doi/10.4171/RMI/932