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GENUS 2 SEMI-REGULAR COVERINGS WITH LIFTING SYMMETRIES

Published online by Cambridge University Press:  01 September 2008

YOLANDA FUERTES  and
ALEXANDER MEDNYKH
YOLANDA FUERTES
Affiliation:
Departamento de Matemáticas, U. Autonoma de Madrid, 28049 Madrid, Spain e-mail: [email protected]
ALEXANDER MEDNYKH
Affiliation:
Sobolev Institute of Mathematics, Novosibirsk State University, 630090, Novosibirsk, Russia e-mail: [email protected]
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Abstract

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In this paper, we obtain algebraic equations for all genus 2 compact Riemann surfaces that admit a semi-regular (or uniform) covering of the Riemann sphere with more than two lifting symmetries. By a lifting symmetry, we mean an automorphism of the target surface which can be lifted to the covering. We restrict ourselves to the genus 2 surfaces in order to make computations easier and to make possible to find their algebraic equations as well. At the same time, the main ingredient (Main Proposition) depends neither on the genus, nor on the order of the group of lifting symmetries. Because of this, the paper can be thought as a generalisation for the non-normal case to the question of lifting automorphisms of a compact Riemann surface to a normal covering, treated, for instance, by E. Bujalance and M. Conder in a joint paper, or by P. Turbek solely.

Keywords

30F1014H3014H45
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 379 - 394
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

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