Conformal actions with prescribed periods on Riemann surfaces

Volume 213 / 2011

G. Gromadzki, W. Marzantowicz Fundamenta Mathematicae 213 (2011), 169-190 MSC: Primary 30F10; Secondary 30F35, 37E30, 14H37. DOI: 10.4064/fm213-2-3


It is a natural question what is the set of minimal periods of a holomorphic maps on a Riemann surface of negative Euler characteristic. Sierakowski studied ordinary holomorphic periods on classical Riemann surfaces. Here we study orientation reversing automorphisms acting on classical Riemann surfaces, and also automorphisms of non-orientable unbordered Klein surfaces to which, following Singerman, we shall refer to as non-orientable Riemann surfaces. We get a complete set of conditions for the existence of conformal actions with a prescribed order and a prescribed set of periods together with multiplicities. This lets us determine the minimal genus of a surface which admits such an action.


  • G. GromadzkiInstitute of Mathematics
    Gdańsk University
    Wita Stwosza 57
    80-952 Gdańsk, Poland
  • W. MarzantowiczFaculty of Mathematics and Computer Science
    Adam Mickiewicz University of Poznań
    Umultowska 87
    61-614 Poznań, Poland

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