Abelian automorphisms groups of Schottky type
Author
Hidalgo, Rubén A.
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/155210.4067/S0716-09172004000300001
Abstract
We study the problem of lifting an Abelian group H of automorphisms of a closed Riemann surface S (containing anticonformals ones) to a suitable Schottky uniformization of S (that is, when H is of Schottky type). If H+ is the index two subgroup of orientation preserving automorphisms of H and R = S/H+, then H induces an anticonformal automorphism ? : R ? R. If ? has fixed points, then we observe that H is of Schottky type. If ? has no fixed points, then we provide a sufficient condition for H to be of Schottky type. We also give partial answers for the excluded cases.