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.
About Aleksandr Pukhlikov
Aleksandr Pukhlikov, University of Liverpool, United Kingdom.Details Book
Author  :  Aleksandr Pukhlikov 
Publisher  :  American Mathematical Society 
Data Published  :  30 July 2013 
ISBN  :  0821894765 
EAN  :  9780821894767 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  367 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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