Conformal actions with prescribed periods on Riemann surfaces

• Autorzy: G. Gromadzki , W. Marzantowicz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 30F10: Compact Riemann surfaces and uniformization
• 14H37: Automorphisms
• 30F35: Fuchsian groups and automorphic functions
• 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 213
• Numer: 2
• Strony: 169-190

Daty

wydano

2011

Twórcy

autor

G. Gromadzki

• Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland

autor

W. Marzantowicz

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University of Poznań, Umultowska 87, 61-614 Poznań, Poland

Identyfikatory

DOI

10.4064/fm213-2-3