Cubic Forms

Algebra, Geometry, Arithmetic

Yu.I. Manin

• Publisher: North Holland
• Year: 1986
• Print ISBN: 9780444878236
• eBook ISBN: 9780080963167
• Edition: 2
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Since this book was first published in English, there has been important progress in a number of related topics. The class of algebraic varieties close to the rational ones has crystallized as a natural domain for the methods developed and expounded in this volume. For this revised edition, the original text has been left intact (except for a few corrections) and has been brought up to date by the addition of an Appendix and recent references.The Appendix sketches some of the most essential new results, constructions and ideas, including the solutions of the Luroth and Zariski problems, the theory of the descent and obstructions to the Hasse principle on rational varieties, and recent applications of K-theory to arithmetic.

Table of contents

• Front Cover
• Cubic Forms: Algebra, Geometry, Arithmetic
• Copyright Page
• CONTENTS
• PREFACE TO THE SECOND EDITION
• INSTRUCTIONS TO THE READER
• INTRODUCTION
• CHAPTER I. CH-QUASIGROUPS AND MOUFANG LOOPS
• CHAPTER II. CLASSES OF POINTS ON CUBIC HYPERSURFACES
• CHAPTER III. TWO-DIMENSIONAL BIRATIONAL GEOMETRY
• CHAPTER IV. THE TWENTY-SEVEN LINES
• CHAPTER V. MINIMAL CUBIC SURFACES
• CHAPTER VI. THE BRAUER–GROTHENDIECK GROUP
• APPENDIX. ALGEBRAIC VARIETIES CLOSE TO THE RATIONAL ONES. ALGEBRA, GEOMETRY, ARITHMETIC
• REFERENCES
• AUTHOR INDEX
• LIST OF SYMBOLS
• SUBJECT INDEX