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ON FIXED POINTS OF DOUBLY SYMMETRIC RIEMANN SURFACES

Published online by Cambridge University Press:  01 September 2008

GRZEGORZ GROMADZKI  and
EWA KOZŁOWSKA-WALANIA
GRZEGORZ GROMADZKI
Affiliation:
Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, Gdańsk 80-952, Poland e-mail: [email protected]
EWA KOZŁOWSKA-WALANIA
Affiliation:
Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, Gdańsk 80-952, Poland e-mail: [email protected]
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Abstract

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In this paper, we study ovals of symmetries and the fixed points of their products on Riemann surfaces of genus g ≥ 2. We show how the number of these points affects the total number of ovals of symmetries. We give a generalisation of Bujalance, Costa and Singerman's theorems in which we show upper bounds for the total number of ovals of two symmetries in terms of g, the order n and the number m of the fixed points of their product, and we show their attainments for n holding some divisibility conditions. Finally, we give an upper bound for m in terms of n and g, and we study conditions under which it has given parity.

Keywords

Primary 30FSecondary 14H
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 371 - 378
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

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