Birational Geometry of Algebraic Varieties (Cambridge Tracts in Mathematics) [Hardcover]

Janos Kollár (Author), Shigefumi Mori (Author)

Book Description

Publication Date: October 28, 1998 | ISBN-10: 0521632773 | ISBN-13: 978-0521632775

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.

Editorial Reviews

Review

"The book under review, written by two of the leaders in the field, is a comprehensive treatment of the minimal model program...invaluable for the more advanced student of the minimal model program, as well as researchers in the field." Mathematical Reviews

"...this book, written by two of the main players in this development, answers a demand for a long awaited introductory textbook for the beginners in this field. The expositon is sufficiently elementary, self-contained and comprehensive, and requires fewer prerequisites, so this book will become a standard reference." Bulletin of the American Mathematical Society

Book Description

One of the major discoveries of the last two decades inalgebraic geometry is the realization that the theory ofminimal models of surfaces can be generalized to higherdimensional varieties. This generalization, called the minimal model program or Mori's program, has developedinto 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 develo ped 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.

Product Details

• Hardcover: 264 pages
• Publisher: Cambridge University Press (October 28, 1998)
• Language: English
• ISBN-10: 0521632773
• ISBN-13: 978-0521632775
• Product Dimensions: 9 x 6.1 x 1 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,662,646 in Books (See Top 100 in Books)

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9 of 9 people found the following review helpful:

5.0 out of 5 stars A gateway to modern birational geometry, November 8, 2002

By A Customer

This review is from: Birational Geometry of Algebraic Varieties (Cambridge Tracts in Mathematics) (Hardcover)

This book provides a neat introduction to (basically) what happened in birational geometry in the '80s. It contains a description of so-called minimal model program which deals which birational classification of complex algebraic varieties. Some level of familiarity with standard algebraic geometry (like what're written in Hartshorne's famous book) is required to be able to read this book. All the important results in MMP were established in this book except the (general) existence of flips in 3 dimension, which doesn't appear anywhere else but the original research articles. One other thing that's missing in this book is discussions of complex analytic methods, which are proved to be extremely useful in dealing with some problems (for example, Fujita conjecture, invariance of plurigenera, so on...).
In conclusion, this is THE must-read book for people who would like to know MMP. It may not be very reader-friendly, but it's a book that you must read if you want to study birational geometry.