Logo - springer
Slogan - springer

Mathematics - Algebra | Birational Geometry, Rational Curves, and Arithmetic

Birational Geometry, Rational Curves, and Arithmetic

Bogomolov, Fedor, Hassett, Brendan, Tschinkel, Yuri (Eds.)

2013, XII, 320 p. 21 illus.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$99.00

(net) price for USA

ISBN 978-1-4614-6482-2

digitally watermarked, no DRM

Included Format: PDF and EPUB

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$129.00

(net) price for USA

ISBN 978-1-4614-6481-5

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

  • ​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

​​​​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.

Content Level » Research

Keywords » arithmetic of higher-dimensional algebraic varieties - birational geometry - cone of curves - rational curves - rationality - unirationality

Related subjects » Algebra - Geometry & Topology - Number Theory and Discrete Mathematics

Table of contents / Preface / Sample pages 

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Algebraic Geometry.