On commutativity and ovals for a pair of symmetries of a Riemann surface

Ewa Kozłowska-Walania. "On commutativity and ovals for a pair of symmetries of a Riemann surface." Colloquium Mathematicae 109.1 (2007): 61-69. <http://eudml.org/doc/284246>.

@article{EwaKozłowska2007,
abstract = {We study the upper bounds for the total number of ovals of two symmetries of a Riemann surface of genus g, whose product has order n. We show that the natural bound coming from Bujalance, Costa, Singerman and Natanzon's original results is attained for arbitrary even n, and in case of n odd, there is a sharper bound, which is attained. We also prove that two (M-q)- and (M-q')-symmetries of a Riemann surface X of genus g commute for g ≥ q+q'+1 (by (M-q)-symmetry we understand a symmetry having g+1-q ovals) and we show that actually, with just one exception for any g > 2, q+q'+1 is the minimal lower bound for g which guarantees the commutativity of two such symmetries.},
author = {Ewa Kozłowska-Walania},
journal = {Colloquium Mathematicae},
keywords = {Harnack's theorem; Riemann surfaces; oval of symmetry; antiholomorphic involution},
language = {eng},
number = {1},
pages = {61-69},
title = {On commutativity and ovals for a pair of symmetries of a Riemann surface},
url = {http://eudml.org/doc/284246},
volume = {109},
year = {2007},
}

TY - JOUR
AU - Ewa Kozłowska-Walania
TI - On commutativity and ovals for a pair of symmetries of a Riemann surface
JO - Colloquium Mathematicae
PY - 2007
VL - 109
IS - 1
SP - 61
EP - 69
AB - We study the upper bounds for the total number of ovals of two symmetries of a Riemann surface of genus g, whose product has order n. We show that the natural bound coming from Bujalance, Costa, Singerman and Natanzon's original results is attained for arbitrary even n, and in case of n odd, there is a sharper bound, which is attained. We also prove that two (M-q)- and (M-q')-symmetries of a Riemann surface X of genus g commute for g ≥ q+q'+1 (by (M-q)-symmetry we understand a symmetry having g+1-q ovals) and we show that actually, with just one exception for any g > 2, q+q'+1 is the minimal lower bound for g which guarantees the commutativity of two such symmetries.
LA - eng
KW - Harnack's theorem; Riemann surfaces; oval of symmetry; antiholomorphic involution
UR - http://eudml.org/doc/284246
ER -