Conformal actions with prescribed periods on Riemann surfaces

G. Gromadzki, and W. Marzantowicz. "Conformal actions with prescribed periods on Riemann surfaces." Fundamenta Mathematicae 213.2 (2011): 169-190. <http://eudml.org/doc/282683>.

@article{G2011,
abstract = {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.},
author = {G. Gromadzki, W. Marzantowicz},
journal = {Fundamenta Mathematicae},
keywords = {automorphism of compact Riemann surfaces; periods of automorphisms},
language = {eng},
number = {2},
pages = {169-190},
title = {Conformal actions with prescribed periods on Riemann surfaces},
url = {http://eudml.org/doc/282683},
volume = {213},
year = {2011},
}

TY - JOUR
AU - G. Gromadzki
AU - W. Marzantowicz
TI - Conformal actions with prescribed periods on Riemann surfaces
JO - Fundamenta Mathematicae
PY - 2011
VL - 213
IS - 2
SP - 169
EP - 190
AB - 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.
LA - eng
KW - automorphism of compact Riemann surfaces; periods of automorphisms
UR - http://eudml.org/doc/282683
ER -