سطوح ریمان و کلاین، خودکارش‌ها، تقارن‌ها و فضاهای مدولی: کنفرانس به افتخار امیلیو بوجالانسه

This volume contains the proceedings of the conference on Riemann and Klein Surfaces, Symmetries and Moduli Spaces, in honor of Emilio Bujalance, held from June 24–28, 2013, at Linköping University. The conference and this volume are devoted to the mathematics that Emilio Bujalance has worked with in the following areas, all with a computational flavor: Riemann and Klein surfaces, automorphisms of real and complex surfaces, group actions on surfaces and topological properties of moduli spaces of complex curves and Abelian varieties. Cover 1 Title page 4 Contents 8 Preface 10 On Jacobians of curves with superelliptic components 12 1. Introduction 12 2. Preliminaries 14 3. Jacobians of superelliptic curves 15 4. Jacobians with superelliptic components 20 Acknowledgments 24 References 24 Superelliptic surfaces as p-gonal surfaces 26 1. Introduction 26 Acknowledgement 26 2. The equation point of view of p-gonal surfaces 26 3. The action point of view of p-gonal surfaces 31 4. Automorphism groups of cyclic n-gonal surfaces 34 5. Families of p-gonal surfaces 37 References 38 Exceptional automorphisms of (generalized) super elliptic surfaces 40 1. Cyclic n-gonal surfaces 40 2. Super-elliptic surfaces 44 3. Discovering exceptional automorphisms 46 4. Classification overview 49 References 52 Symmetric group actions on Jacobian varieties 54 1. Introduction 54 2. Results 56 3. Summary. 65 References 67 Normal coverings of hyperelliptic real Riemann surfaces 70 1. Introduction 70 2. Normal coverings of hyperelliptic Riemann surfaces 71 3. Normal coverings of hyperelliptic real Riemann surfaces 74 Acknowledgement 86 References 86 Large group actions on surfaces 88 1. Introduction 88 2. Further background 90 3. Computations and observations 93 4. Related matters 96 5. Some open questions 97 References 107 Maximal bordered surface groups versus maximal handlebody groups 110 1. Introduction 110 2. The genera of maximal handlebody groups 112 3. Concluding remarks 115 References 116 Maximal and Non-maximal NEC and Fuchsian groups uniformizing Klein and Riemann surfaces 118 1. Introduction 118 2. Non-euclidean crystallographic and Fuchsian groups 119 3. Teichmüller and Moduli spaces of Fuchsian and NEC\ groups 120 4. Maximal NEC groups 121 5. Applications 123 References 127 On the minimum genus problem on bordered Klein surfaces for automorphisms of even order 130 1. Introduction 130 2. The computation of p++(N,k) 131 3. The computation of p+−(N,k) 134 4. The computation of p−(N,k) 137 5. The values for N