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

• Autorzy: Ewa Kozłowska-Walania
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 14H37: Automorphisms
• 30F50: Klein surfaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 109
• Numer: 1
• Strony: 61-69

Daty

wydano

2007

Twórcy

autor

Ewa Kozłowska-Walania

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

Identyfikatory

DOI

10.4064/cm109-1-5