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On real forms of a complex algebraic curve

Part of: Other groups of matrices Special aspects of infinite or finite groups Curves Riemann surfaces

Published online by Cambridge University Press:  09 April 2009

E. Bujalance ,
G. Gromadzki  and
M. Izquierdo
E. Bujalance
Affiliation:
Depto de Matemáticas Fund. UNED c/ Senda del Rey s/n 28040 MadridSpain e-mail: eb@mat.uned.es
G. Gromadzki
Affiliation:
Institute of Mathematics UG Wita Stwosza57 80-952 GdańskPoland e-mail: greggrom@ksinet.univ.gda.pl
M. Izquierdo
Affiliation:
Department of Mathematics Mälardalen University721 23 VästeråsSweden e-mail: mio@mdh.se
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Abstract

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Two projective nonsingular complex algebraic curves X and Y defined over the field R of real numbers can be isomorphic while their sets X(R) and Y(R) of R-rational points could be even non homeomorphic. This leads to the count of the number of real forms of a complex algebraic curve X, that is, those nonisomorphic real algebraic curves whose complexifications are isomorphic to X. In this paper we compute, as a function of genus, the maximum number of such real forms that a complex algebraic curve admits.

MSC classification

Secondary: 14H45: Special curves and curves of low genus 20H10: Fuchsian groups and their generalizations 30F50: Klein surfaces 20F05: Generators, relations, and presentations

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 1 , February 2001 , pp. 134 - 142
Copyright
Copyright © Australian Mathematical Society 2001

References

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