Overview
- Leading experts report on recent advances in higher-dimensional birational geometry, with special regard to arithmetic applications
- Highlights the tight connections between arithmetic and geometry
- Documents the central role of the theory of rational curves
- Includes supplementary material: sn.pub/extras
Part of the book series: Simons Symposia (SISY)
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Table of contents (12 chapters)
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Front Matter
Keywords
About this book
​​​​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.
Editors and Affiliations
About the editors
Bibliographic Information
Book Title: Birational Geometry, Rational Curves, and Arithmetic
Editors: Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel
Series Title: Simons Symposia
DOI: https://doi.org/10.1007/978-1-4614-6482-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-6481-5Published: 17 May 2013
Softcover ISBN: 978-1-4939-0158-6Published: 12 June 2015
eBook ISBN: 978-1-4614-6482-2Published: 17 May 2013
Series ISSN: 2365-9564
Series E-ISSN: 2365-9572
Edition Number: 1
Number of Pages: IX, 319
Topics: Algebraic Geometry, Number Theory, Geometry