Birationally rigid varieties
著者
書誌事項
Birationally rigid varieties
（Mathematical surveys and monographs, v. 190）
American Mathematical Society, c2013
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注記
Includes bibliographical references (p. 359-365) and index
内容説明・目次
内容説明
Birational rigidity is a striking and mysterious phenomenon in higher-dimensional algebraic geometry. It turns out that certain natural families of algebraic varieties (for example, three-dimensional quartics) belong to the same classification type as the projective space but have radically different birational geometric properties. In particular, they admit no non-trivial birational self-maps and cannot be fibred into rational varieties by a rational map. The origins of the theory of birational rigidity are in the work of Max Noether and Fano; however, it was only in 1970 that Iskovskikh and Manin proved birational superrigidity of quartic three-folds. This book gives a systematic exposition of, and a comprehensive introduction to, the theory of birational rigidity, presenting in a uniform way, ideas, techniques, and results that so far could only be found in journal papers. The recent rapid progress in birational geometry and the widening interaction with the neighboring areas generate the growing interest to the rigidity-type problems and results. The book brings the reader to the frontline of current research. It is primarily addressed to algebraic geometers, both researchers and graduate students, but is also accessible for a wider audience of mathematicians familiar with the basics of algebraic geometry.
目次
Table of Contents:
Introduction
The rationality problem
The method of maximal singularities
Hypertangent divisors
Rationally connected fibre spaces
Fano fibre spaces of P1
Del Pezzo fibrations
Fano direct products
Double spaces of index two
Bibliography Index
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