Introduction to the Mori Program [Hardcover]

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.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

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 authors personal notes. One of its greatest l_