TY - JOUR AU - Hidalgo, Rubén A. PY - 2017/05/22 Y2 - 2024/03/29 TI - Abelian automorphisms groups of Schottky type JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 23 IS - 3 SE - DO - 10.4067/S0716-09172004000300001 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1552 SP - 187-203 AB - <span class="fontstyle0">We study the problem of lifting an Abelian group </span><span class="fontstyle2">H </span><span class="fontstyle0">of automorphisms of a closed Riemann surface </span><span class="fontstyle2">S </span><span class="fontstyle0">(containing anticonformals ones) to a suitable Schottky uniformization of </span><span class="fontstyle2">S </span><span class="fontstyle0">(that is, when </span><span class="fontstyle2">H </span><span class="fontstyle0">is of Schottky type). If </span><span class="fontstyle2">H</span><span class="fontstyle3">+ </span><span class="fontstyle0">is the index two subgroup of orientation preserving automorphisms of </span><span class="fontstyle2">H </span><span class="fontstyle0">and </span><span class="fontstyle2">R </span><span class="fontstyle4">= </span><span class="fontstyle2">S/H</span><span class="fontstyle3">+</span><span class="fontstyle0">, then </span><span class="fontstyle2">H </span><span class="fontstyle0">induces an anticonformal automorphism </span><span class="fontstyle2">? </span><span class="fontstyle4">: </span><span class="fontstyle2">R </span><span class="fontstyle5">? </span><span class="fontstyle2">R</span><span class="fontstyle0">. If </span><span class="fontstyle2">? </span><span class="fontstyle0">has fixed points, then we observe that </span><span class="fontstyle2">H </span><span class="fontstyle0">is of Schottky type. If </span><span class="fontstyle2">? </span><span class="fontstyle0">has no fixed points, then we provide a sufficient condition for </span><span class="fontstyle2">H </span><span class="fontstyle0">to be of Schottky type. We also give partial answers for the excluded cases.</span> ER -