**Contemporary Mathematics**

Volume: 397;
2006;
236 pp;
Softcover

MSC: Primary 30; 14;

**Print ISBN: 978-0-8218-3855-6
Product Code: CONM/397**

List Price: $80.00

AMS Member Price: $64.00

MAA Member Price: $72.00

**Electronic ISBN: 978-0-8218-7987-0
Product Code: CONM/397.E**

List Price: $75.00

AMS Member Price: $60.00

MAA Member Price: $67.50

# The Geometry of Riemann Surfaces and Abelian Varieties

Share this page *Edited by *
*José M. Muñoz Porras; Sorin Popescu; Rubí E. Rodríguez*

Most of the papers in this book deal with the theory of Riemann surfaces (moduli problems, automorphisms, etc.), abelian varieties, theta functions, and modular forms. Some of the papers contain surveys on the recent results in the topics of current interest to mathematicians, whereas others contain new research results.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry and complex geometry.

# Table of Contents

## The Geometry of Riemann Surfaces and Abelian Varieties

- Contents vii8 free
- Preface ix10 free
- Möbius transformations of the circle form a maximal convergence group 112 free
- On the polar linear system of a foliation by curves in a projective space 718
- Birational classification of hyperelliptic real algebraic curves 1526
- The genus two Jacobians that are isomorphic to a product of elliptic curves 2738
- Vanishing thetanulls and Jacobians 3748
- Theta functions, geometric quantization and unitary Schottky bundles 5566
- 1. Introduction 5566
- 2. Vector bundles and theta functions 5667
- 3. Geometric quantization in a real polarization 5768
- 4. Trinion decompositions and Schottky bundles 6071
- 5. Spin networks 6273
- 6. Holomorphic polarization 6677
- 7. The BKS pairing and the matrix S 6879
- 8. Acknowledgments 7081
- References 7081

- Smooth double coverings of hyperelliptic curves 7384
- Planar families of discrete groups 7990
- Generalized addition formulae for theta functions 89100
- Curves with a group action and Galois covers via infinite Grassmannians 105116
- Some recent results on the irreducible components of the singular locus of Ag 119130
- A note on the arithmetic genus of reducible plane curves 127138
- Teichmüller curves defined by characteristic origamis 133144
- Lowest uniformizations of compact real surfaces 145156
- Principal polarizations on products of elliptic curves 153164
- An approach to a 2-dimensional Contou-Carrère symbol 163174
- Prym varieties and fourfold covers II: The dihedral case 177188
- Examples for Veech groups of origamis 193204
- Genus 2 translation surfaces with an order 4 automorphism 207218
- The Pfaffian structure defining a Prym theta divisor 215226