Birationally rigid varieties
 Author/Creator
 Pukhlikov, Aleksandr V., 1962
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2013]
 Copyright notice
 ©2013
 Physical description
 vi, 367 pages ; 26 cm.
 Series
 Mathematical surveys and monographs ; v. 190.
Access
Available online

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QA3 .A4 V.190
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Contributors
 Contributor
 American Mathematical Society.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 359365) and index.
 Contents

 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 Birational rigidity is a striking and mysterious phenomenon in higherdimensional algebraic geometry. It turns out that certain natural families of algebraic varieties (for example, threedimensional quartics) belong to the same classification type as the projective space but have radically different birational geometric properties. In particular, they admit no nontrivial birational selfmaps 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 threefolds. 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 rigiditytype 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.
(source: Nielsen Book Data)
Subjects
 Subject
 Geometry, Algebraic.
Bibliographic information
 Publication date
 2013
 Responsibility
 Aleksandr Pukhlikov.
 Series
 Mathematical surveys and monographs ; v. 190
 ISBN
 9780821894767
 0821894765