Rational and Nearly Rational Varieties [Hardcover]

Modern theory of rational and nearly rational varieties. Many problems with solutions make it ideal for graduate courses.Arising from a summer school course taught by Kollar, this book develops the modern theory of rational varieties at a level that will particularly suit graduate students. Kollár'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. These will help students reach the stage where they can begin to tackle contemporary research problems in this area.Arising from a summer school course taught by Kollar, this book develops the modern theory of rational varieties at a level that will particularly suit graduate students. Kollár'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. These will help students reach the stage where they can begin to tackle contemporary research problems in this area.Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational varieties at a level appropriate for graduate study. Kollár'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.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.'& a beautiful and ample introduction to the interesting topic of rational and 'nearly rational' varieties and it will be a valuable reference for a wide audilcs