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Technical Rational and Nearly Rational Varieties
Posted on 2010-07-27
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More János Kollár, Karen E. Smith, Alessio Corti, "Rational and Nearly Rational Varieties" 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. Over one hundred exercises with fully worked out solutions • First elementary treatment of rationality questions • Mixture of classical and modern methods 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. Review '… 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 audience.' Zentralblatt MATH Download
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