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Archiv der Mathematik

, Volume 95, Issue 5, pp 481–492

First Online: 06 November 2010Received: 11 March 2010Revised: 21 July 2010


A Riemann surface is said to be pseudo-real if it admits an antiholomorphic automorphism but not an antiholomorphic involution also known as a symmetry. The importance of such surfaces comes from the fact that in the moduli space of compact Riemann surfaces of given genus, they represent the points with real moduli. Clearly, real surfaces have real moduli. However, as observed by Earle, the converse is not true. Moreover, it was shown by Seppälä that such surfaces are coverings of real surfaces. Here we prove that the latter may always be assumed to be purely imaginary. We also give a characterization of finite groups being groups of automorphisms of pseudo-real Riemann surfaces. Finally, we solve the minimal genus problem for the cyclic case.

Mathematics Subject Classification 2000Primary 30F Secondary 14H C. Baginski was supported by the grant S-W I -3-2008 of Bialystok University of Technology, Bialystok, Poland.

G. Gromadzki was supported by the Research Grant N N201 366436 of the Polish Ministry of Sciences and Higher Education.

KeywordsPseudo-real Riemann surfaces Pseudo-symmetric Riemann surfaces Automorphisms of Riemann surfaces Anticonformal automorphisms Symmetric Riemann surfaces Symmetry of a Riemann surface Real algebraic curves Complex algebraic curves with real moduli Fuchsian and noneuclidean crystallographic groups NEC  Download to read the full article text

Autor: Czesław Bagiński - Grzegorz Gromadzki


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