Birational Geometry, Rational Curves, and Arithmetic

Nonfiction, Science & Nature, Mathematics, Number Theory, Geometry
Cover of the book Birational Geometry, Rational Curves, and Arithmetic by , Springer New York
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: ISBN: 9781461464822
Publisher: Springer New York Publication: May 17, 2013
Imprint: Springer Language: English
Author:
ISBN: 9781461464822
Publisher: Springer New York
Publication: May 17, 2013
Imprint: Springer
Language: English

​​​​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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

​​​​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.

More books from Springer New York

Cover of the book Ultrasound in the Intensive Care Unit by
Cover of the book Reproductive Endocrinology and Infertility by
Cover of the book Microsurgery for Cerebral Ischemia by
Cover of the book How James Watt Invented the Copier by
Cover of the book Please God Send Me a Wreck by
Cover of the book Residue Reviews by
Cover of the book Public Choice, Past and Present by
Cover of the book Pediatric Nuclear Medicine by
Cover of the book Scandinavian Colonialism and the Rise of Modernity by
Cover of the book Nanotechnology in Dermatology by
Cover of the book Calculus With Applications by
Cover of the book Laboratory Protocols in Fungal Biology by
Cover of the book Introduction to Molecular Medicine by
Cover of the book Autoimmunity and the Pathogenesis of Diabetes by
Cover of the book College Sports Inc. by
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy