Conformal actions with prescribed periods on Riemann surfaces

G. Gromadzki¹ ; W. Marzantowicz²

¹ Institute of Mathematics Gdańsk University Wita Stwosza 57 80-952 Gdańsk, Poland
² Faculty of Mathematics and Computer Science Adam Mickiewicz University of Poznań Umultowska 87 61-614 Poznań, Poland

Fundamenta Mathematicae, Tome 213 (2011) no. 2, pp. 169-190.

Résumé

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.

Détail

DOI : 10.4064/fm213-2-3

Keywords: natural question what set minimal periods holomorphic maps riemann surface negative euler characteristic sierakowski studied ordinary holomorphic periods classical riemann surfaces here study orientation reversing automorphisms acting classical riemann surfaces automorphisms non orientable unbordered klein surfaces which following singerman shall refer non orientable riemann surfaces get complete set conditions existence conformal actions prescribed order prescribed set periods together multiplicities lets determine minimal genus surface which admits action