Rational and nearly rational varieties

Author(s)

• Kollár, János
• Smith, Karen E.
• Corti, Alessio

Bibliographic Information

Rational and nearly rational varieties

János Kollár, Karen E. Smith, and Alessio Corti

（Cambridge studies in advanced mathematics, 92）

Cambridge University Press, 2004

• : hardback

Note

Bibliography: p. 228-231

Includes index

Description and Table of Contents

Description

The most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications where algebraic varieties appear in mathematics and the sciences, we see rational ones emerging as the most interesting examples. The authors have given an elementary treatment of rationality questions using a mix of classical and modern methods. Arising from a summer school course taught by Janos Kollar, this book develops the modern theory of rational and nearly rational varieties at a level that will particularly suit graduate students. There are numerous examples and exercises, all of which are accompanied by fully worked out solutions, that will make this book ideal as the basis of a graduate course. It will act as a valuable reference for researchers whilst helping graduate students to reach the point where they can begin to tackle contemporary research problems.

Table of Contents

• Introduction
• 1. Examples of rational varieties
• 2. Cubic surfaces
• 3. Rational surfaces
• 4. Nonrationality and reduction modulo p
• 5. The Noether-Fano method
• 6. Singularities of pairs
• 7. Solutions to exercises.

by "Nielsen BookData"

Details

• NCID: BA66788835
• ISBN:
  • 0521832071
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge, U.K.
• Pages/Volumes: vi, 235 p.
• Size: 24 cm
• Classification:
  • DC21 : 512
• Subject Headings:
  • LCSH : Varieties (Universal algebra)
• Parent Bibliography ID:
  • BA00109761