| Description |
1 online resource (xiv, 218 pages) : illustrations |
| Series |
London Mathematical Society lecture note series ; 230 |
|
London Mathematical Society lecture note series ; 230.
|
| Contents |
Ch. 1. Curves of genus 2 -- Ch. 2. Construction of the jacobian -- Ch. 3. The Kummer surface -- Ch. 4. The dual of the Kummer -- Ch. 5. Weddle's surface -- Ch. 6. [actual symbol not reproducible] -- Ch. 7. The jacobian over local fields. Formal groups -- Ch. 8. Torsion -- Ch. 9. The isogeny. Theory -- Ch. 10. The isogeny. Applications -- Ch. 11. Computing the Mordell-Weil group -- Ch. 12. Heights -- Ch. 13. Rational points. Chabauty's Theorem -- Ch. 14. Reducible jacobians -- Ch. 15. The endomorphism ring -- Ch. 16. The desingularized Kummer -- Ch. 17. A neoclassical approach -- Ch. 18. Zukunftsmusik -- Appendix I. MAPLE programs -- Appendix II. Files available by anonymous ftp |
| Summary |
The number theoretic properties of curves of genus 2 are attracting increasing attention. This book provides new insights into this subject; much of the material here is entirely new, and none has appeared in book form before. Included is an explicit treatment of the Jacobian, which throws new light onto the geometry of the Kummer surface. The Mordell-Weil group can then be determined for many curves, and in many non-trivial cases all rational points can be found. The results exemplify the power of computer algebra in diophantine contexts, but computer expertise is not assumed in the main text. Number theorists, algebraic geometers and workers in related areas will find that this book offers unique insights into the arithmetic of curves of genus 2 |
| Bibliography |
Includes bibliographical references (pages 207-218) and index |
| Notes |
Print version record |
| Subject |
Curves, Algebraic.
|
|
MATHEMATICS -- Geometry -- Algebraic.
|
|
Curves, Algebraic
|
|
Arithmetik
|
|
Algebraische Kurve
|
|
Geschlecht Mathematik
|
|
Algebraïsche krommen.
|
|
Rekenkunde.
|
|
Courbes algébriques.
|
|
Géométrie algébrique.
|
| Form |
Electronic book
|
| Author |
Flynn, E. V
|
| ISBN |
9781107362178 |
|
1107362172 |
|
