The number theoretic properties of curves of genus 2 are attracting increasing attention. This book provides insights into this subject. Number theorists, algebraic geometers and workers in related areas will find that this book offers insights into the arithmetic of curves of genus 2. It includes an explicit treatment of the Jacobian.
A unique insight into the topic of curves of genus 2, by two of the world??'s leading practitioners.
Background and conventions; 1. Curves of genus 2; 2. Construction of the jacobian; 3. The Kummer surface; 4. The dual of the Kummer; 5. Weddle's surface; 6. G/2G; 7. The jacobian over local fields; Formal groups; 8. Torsion; 9. The isogeny; Theory; 10. The isogeny; Applications; 11. Computing the Mordell-Weil group; 12. Heights; 13. Rational points Chabauty's theorem; 14. Reducible jacobians; 15. The endomorphism ring; 16. The desingularized Kummer; 17. A neoclassical approach; 18. Zukunftsmusik; Appendix 1. MAPLE programs; Appendix 2. Files available by FTP.