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Cubic Forms - 2nd Edition - ISBN: 9780444878236, 9780080963167

Cubic Forms, Volume 4

2nd Edition

Algebra, Geometry, Arithmetic

Author: Yu.I. Manin
eBook ISBN: 9780080963167
Hardcover ISBN: 9780444878236
Paperback ISBN: 9780444558138
Imprint: North Holland
Published Date: 1st February 1986
Page Count: 325
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Table of Contents

CH-Quasigroups and Moufang Loops. Classes of Points on Cubic Hypersurfaces. Two-Dimensional Birational Geometry. The Twenty-Seven Lines. Minimal Cubic Surfaces. The Brauer-Grothendieck Group.
Appendix: Algebraic Varieties Close to the Rational Ones. Algebra, Geometry, Arithmetic. Galois Cohomology, Picard Groups and Birational Geometry. The Hasse Principle and Descent on Rational Varieties. Geometry of Rational Surfaces. Complements. The Luroth Problem and the Zariski Problem in Dimension 3. Rational Points and Equivalence Relations. Cubic Surfaces and Commutative Loops (CML). References. Subject Index.


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.


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© North Holland 1986
1st February 1986
North Holland
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Hardcover ISBN:
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About the Author

Yu.I. Manin