The Geometry of Riemann Surfaces and Abelian Varieties

Preface ix

M¨obius transformations of the circle form a maximal convergence group

Ara Basmajian and Mahmoud Zeinalian 1

On the polar linear system of a foliation by curves in a projective space

Antonio Campillo and Jorge Olivares 7

Birational classification of hyperelliptic real algebraic curves

Francisco Javier Cirre 15

The genus two Jacobians that are isomorphic to a product of elliptic curves

Clifford J. Earle 27

Vanishing thetanulls and Jacobians

Hershel M. Farkas 37

Theta functions, geometric quantization and unitary Schottky bundles

Carlos Florentino, Jos´e Mour˜ao and Jo˜ao P. Nunes 55

Smooth double coverings of hyperelliptic curves

Yolanda Fuertes and Gabino Gonz´alez-Diez 73

Planar families of discrete groups

Jane Gilman and Linda Keen 79

Generalized addition formulae for theta functions

E. G´omez Gonz´alez and C. Gonz´alez-Mart´ınez 89

Curves with a group action and Galois covers via infinite Grassmannians

E. G´omez Gonz´alez and F. J. Plaza Mart´ın 105

Some recent results on the irreducible components of the singular locus of Ag

V. Gonz´alez-Aguilera, J.M. Mu˜noz-Porras

and Alexis G. Zamora 119

A note on the arithmetic genus of reducible plane curves

M. R. Gonzalez-Dorrego 127

Teichm¨uller curves defined by characteristic origamis

Frank Herrlich 133

Lowest uniformizations of compact real surfaces

Rub´en A. Hidalgo and Bernard Maskit 145

vii

viii CONTENTS

Principal polarizations on products of elliptic curves

Herbert Lange 153

An approach to a 2-dimensional Contou-Carr`ere symbol

Fernando Pablos Romo 163

Prym varieties and fourfold covers II: The dihedral case

Sev´ın Recillas and Rub´ı E. Rodr´ıguez 177

Examples for Veech groups of origamis

Gabriela Schmith¨usen 193

Genus 2 translation surfaces with an order 4 automorphism

Robert Silhol 207

The Pfaffian structure defining a Prym theta divisor

Roy Smith and Robert Varley 215