Overview

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.

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9780511526084

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'... this textbook provides an excellent treatment of the subject of the basic algebraic geometry (and arithmetic) of genus 2 curves and would serve as a useful introductory text for graduate students.' A Maciocia, Proceedings of the Edinburgh Mathematical Society '... an explicit treatment.' L'Enseignement Mathematique 'It is clear that this often subtle and witty book is required reading for those working in the field.' J. Schoissengeier, Monatshefte fur Mathematik '... the authors adopt a down-to-earth approach, assuming a fair background in algebraic geometry, but explaining carefully the tools used.' Mathematika 'The book is accessible without too many prerequisutes ... As a readable introduction to an exciting area of research in which there are may interesting questions still to be answered, the book is to be strongly recommended.' Bulletin of the London Mathematics Society

'... this textbook provides an excellent treatment of the subject of the basic algebraic geometry (and arithmetic) of genus 2 curves and would serve as a useful introductory text for graduate students.' A Maciocia, Proceedings of the Edinburgh Mathematical Society '... an explicit treatment.' L'Enseignement Mathematique 'It is clear that this often subtle and witty book is required reading for those working in the field.' J. Schoissengeier, Monatshefte fur Mathematik '... the authors adopt a down-to-earth approach, assuming a fair background in algebraic geometry, but explaining carefully the tools used.' Mathematika 'The book is accessible without too many prerequisutes ... As a readable introduction to an exciting area of research in which there are may interesting questions still to be answered, the book is to be strongly recommended.' Bulletin of the London Mathematics Society The volume is a comprehensive introduction to the burgeoning theory of computations on genus 2 curves and jacobians, clearly written and chock full of first-rate mathematical insights; it will certainly be the primary reference source for anyone wishing to study the subject. Joseph H. Silverman, Mathematical Reviews

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