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portada Birationally Rigid Varieties (en Inglés)
Formato
Libro Físico
Colección
Mathematical Surveys and Monographs
Año
2013
Idioma
Inglés
N° páginas
367
Encuadernación
Tapa Dura
ISBN13
9780821894767

Birationally Rigid Varieties (en Inglés)

Aleksandr Pukhlikov (Autor) · American Mathematical Society · Tapa Dura

Birationally Rigid Varieties (en Inglés) - Aleksandr Pukhlikov

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Reseña del libro "Birationally Rigid Varieties (en Inglés)"

Provides 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 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.

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.

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