Cambridge Studies in Advanced Mathematics

1 primary work • 2 total works

Rational and Nearly Rational Varieties ICM Edition

by Karen E. Smith and Alessio Corti

Published 23 July 2010

Arising from a summer school course taught by Janos Kollar, this book develops the modern theory of rational varieties at a level appropriate for graduate study. Kollar's original course has been developed, with his co-authors, into a state-of-the-art treatment of the classification of algebraic varieties. The authors have included numerous exercises with solutions, which help students reach the stage where they can begin to tackle related contemporary research problems.

Rational and Nearly Rational Varieties

by Janos Kollar, Karen E. Smith, and Alessio Corti

Published 1 July 2003

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.