Birational Geometry of Algebraic Varieties

Birational Geometry of Algebraic Varieties
Author: Janos Kollár
Publisher: Cambridge University Press
Total Pages: 254
Release: 2010-03-24
Genre: Mathematics
ISBN: 9780511662560


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One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.


Birational Geometry of Algebraic Varieties
Language: en
Pages: 254
Authors: Janos Kollár
Categories: Mathematics
Type: BOOK - Published: 2010-03-24 - Publisher: Cambridge University Press

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One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized t
Algebraic Geometry
Language: en
Pages: 357
Authors: S. Iitaka
Categories: Mathematics
Type: BOOK - Published: 2011-10-14 - Publisher: Springer

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The aim of this book is to introduce the reader to the geometric theory of algebraic varieties, in particular to the birational geometry of algebraic varieties.
Rational Curves on Algebraic Varieties
Language: en
Pages: 330
Authors: Janos Kollar
Categories: Mathematics
Type: BOOK - Published: 2013-04-09 - Publisher: Springer Science & Business Media

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The aim of this book is to provide an introduction to the structure theory of higher dimensional algebraic varieties by studying the geometry of curves, especia
Birational Geometry, Rational Curves, and Arithmetic
Language: en
Pages: 324
Authors: Fedor Bogomolov
Categories: Mathematics
Type: BOOK - Published: 2013-05-17 - Publisher: Springer Science & Business Media

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​​​​This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry.
Automorphisms in Birational and Affine Geometry
Language: en
Pages: 509
Authors: Ivan Cheltsov
Categories: Mathematics
Type: BOOK - Published: 2014-06-11 - Publisher: Springer

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The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geome