Rational and Nearly Rational Varieties

Janos Kollar, Karen E. Smith, Alessio Corti - Collection Cambridge Studies in Advanced Mathematics

235 pages, parution le 08/04/2004

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Résumé

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 János Kollár, 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.

Sommaire

Introduction
Examples of rational varieties
Cubic surfaces
Rational surfaces
Nonrationality via reduction modulo p
The noether-fano mehthod for proving nonrationality
Singularities of pairs
Solutions to exercises

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Janos Kollar, Karen E. Smith, Alessio Corti
Collection	Cambridge Studies in Advanced Mathematics
Parution	08/04/2004
Nb. de pages	235
Format	15,5 x 23,5
Couverture	Relié
Poids	575g
Intérieur	Noir et Blanc
EAN13	9780521832076
ISBN13	978-0-521-83207-6