Introduction to the Mori Program

ISBN-13: 9780387984650 / Angielski / Twarda / 2002 / 478 str.

Kenji Matsuki

Opis

Mori's Program is a fusion of the so-called Minimal Model Program and the IItaka Program toward the biregular and/or birational classification of higher dimensional algebraic varieties. The author presents this theory in an easy and understandable way with lots of background motivation. Prerequisites are those covered in Hartshorne's book "Algebraic Geometry." This is the first book in this extremely important and active field of research and will become a key resource for graduate students wanting to get into the area.

Recenzje

From the reviews:

"This text of nearly 500 pages represents the author turning into book form the collection of personal notes he made when understanding the various aspects of what he refers to as the Mori program. ... This book ... is self-contained ... . The book is written in a very didactic style ... . The book starts and finishes with cogent illustrations of the theory ... ." (W. Pelham, Nieuw Archief voor Wiskunde, Vol. 4 (3), 2003)

"The book under review is an enthusiastic introduction to the minimal model program, or Mori program. ... this work is the first attempt to give a predigested introduction to this beautiful realm of mathematics. The book has the rare quality of introducing in a simple and stimulating way a difficult and very often technical subject." (Massimiliano Mella, Mathematical Reviews, 2002 m)

"Mori theory has been one of the most active areas of algebraic geometry in the past twenty years. ... This book grew out of author's personal notes. One of its greatest strengths is that it is probably the easiest-to-read book on the subject. It is written in a clear, comprehensible style, and the author's love of the subject always shines through. ... The book is aimed at graduate students ... but anyone wanting to learn about the Mori's program will find it useful." (Gabor Megyesi, Bulletin of the London Mathematical Society, Issue 35, 2003)

"This textbook is a highly welcome novelty in the literature on algebraic geometry. Written in a very lucid, rigorous and comprehensive style, this book helps to make the advanced topic of Mori theory a lot more attractive and accessible ... . The book is fairly self-contained ... . The user friendliness of K. Matsuki's textbook ... is bolstered up by detailed references to the literature for each single chapter, a complete list of notations used in the course of the text, and an extensive bibliography." (Werner Kleinert, Zentralblatt MATH, Vol. 988 (13), 2002)

"The purpose of this book is to give a comprehensible account of what is called the Mori Program ... . The author presents this theory in an easy and understandable way with lots of background motivation ... . It is the first 'friendly' book in this extremely important and active area of research and will become a key resource for graduate students wanting to enter this area." (L'Enseignement Mathematique, Vol. 48 (1-2), 2002)

Spis treści

Introduction * Birational Geometry of Surfaces * Logarithmic Category * Overview of the Mori Program * Singularities * Vanishing Theorems * Base Point Freeness of Linear Systems * Cone Theorem. Contraction Theorem * Flip * Cone Theorem Revisited * Logarithmic Mori's Program * Birational Relations among Minimal Models * Birational Relations among Mori Fiber Spaces * Birational Geometry of Toric Varieties