@article{Tyszkowska_2017, title={On symmetries of pq-hyperelliptic Riemann surfaces}, volume={25}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1543}, DOI={10.4067/S0716-09172006000200004}, abstractNote={<span class="fontstyle0">A symmetry of a Riemann surface </span><span class="fontstyle2">X </span><span class="fontstyle0">is an antiholomorphic involution </span><span class="fontstyle2">ø</span><span class="fontstyle0">. The species of </span><span class="fontstyle2">ø </span><span class="fontstyle0">is the integer </span><span class="fontstyle2">ek</span><span class="fontstyle0">, where </span><span class="fontstyle2">k </span><span class="fontstyle0">is the number of connected components in the set </span><span class="fontstyle3">Fix(</span><span class="fontstyle2">ø</span><span class="fontstyle3">) </span><span class="fontstyle0">of fixed points of </span><span class="fontstyle2">ø </span><span class="fontstyle0">and </span><span class="fontstyle2">ε </span><span class="fontstyle3">= </span><span class="fontstyle4">-</span><span class="fontstyle3">1 </span><span class="fontstyle0">if </span><span class="fontstyle2">X </span><span class="fontstyle4">\ </span><span class="fontstyle3">Fix(</span><span class="fontstyle2">ø</span><span class="fontstyle3">) </span><span class="fontstyle0">is connected and </span><span class="fontstyle2">ε </span><span class="fontstyle3">= 1 </span><span class="fontstyle0">otherwise. A compact Riemann surface </span><span class="fontstyle2">X </span><span class="fontstyle0">of genus </span><span class="fontstyle2">g &gt; </span><span class="fontstyle3">1 </span><span class="fontstyle0">is said to be </span><span class="fontstyle2">p</span><span class="fontstyle0">-hyperelliptic if it admits a conformal involution </span><span class="fontstyle2">p</span><span class="fontstyle0">, called a </span><span class="fontstyle2">p</span><span class="fontstyle0">-hyperelliptic involution, for which </span><span class="fontstyle2">X/p </span><span class="fontstyle0">is an orbifold of genus </span><span class="fontstyle2">p</span><span class="fontstyle0">. Symmetries of </span><span class="fontstyle2">p</span><span class="fontstyle0">-hyperelliptic Riemann surfaces has been studied by Klein for </span><span class="fontstyle2">p </span><span class="fontstyle3">= 0 </span><span class="fontstyle0">and by Bujalance and Costa for </span><span class="fontstyle2">p &gt; </span><span class="fontstyle3">0</span><span class="fontstyle0">. Here we study the species of symmetries of so called </span><span class="fontstyle2">pq</span><span class="fontstyle0">-hyperelliptic surface defined as a Riemann surface which is </span><span class="fontstyle2">p</span><span class="fontstyle0">- and </span><span class="fontstyle2">q</span><span class="fontstyle0">-hyperelliptic simultaneously.</span>}, number={2}, journal={Proyecciones (Antofagasta, On line)}, author={Tyszkowska, Ewa}, year={2017}, month={May}, pages={179-189} }