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This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families.
This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.
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About the Author:
F. Bogomolov is Professor at the Courant Institute, NYU. He is best known for his pioneering work on hyperkähler manifolds. B. Hassett is Professor and Chair of the department of Mathematics at Rice University. He published two books and around 50 papers on Algebraic and Arithmetic Geometry. Yuri Tschinkel is Professor at the Courant Institute, NYU and Director of the Mathematics and the Physical Sciences Division at the Simons Foundation.
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- PublisherSpringer
- Publication date2015
- ISBN 10 1493901583
- ISBN 13 9781493901586
- BindingPaperback
- Number of pages328
- EditorBogomolov Fedor, Hassett Brendan, Tschinkel Yuri
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Birational Geometry, Rational Curves, and Arithmetic
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Book Description Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families.This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program. Seller Inventory # 9781493901586
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Birational Geometry, Rational Curves, and Arithmetic
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Book Description Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware - This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families.This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program. 332 pp. Englisch. Seller Inventory # 9781493901586
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Book Description Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Leading experts report on recent advances in higher-dimensional birational geometry, with special regard to arithmetic applicationsHighlights the tight connections between arithmetic and geometryDocuments the central role of the theory of r. Seller Inventory # 33841340
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Book Description Condition: New. New! This book is in the same immaculate condition as when it was published. Seller Inventory # 353-1493901583-new
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Book Description Paperback. Condition: Brand New. 320 pages. 9.25x6.10x0.75 inches. In Stock. Seller Inventory # zk1493901583
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