Introduction to the Mori Program

The purpose of this book is to give a comprehensible account of what is called Mori's Program. 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." It is the first book in this extremely important and active area of research and will become a key resource for graduate students wanting to get into the area.

The first book in this extremely important and active area of research; likely to become a key resource Author presents the theory in an easy and understandable way with lots of background motivation Prerequisites are kept to a minimum, enabling readers to quickly orient themselves with the theory

Klappentext

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.

Inhalt
Introduction: The Tale of the Mori Program.- 1 Birational Geometry of Surfaces.- 2 Logarithmic Category.- 3 Overview of the Mori Program.- 4 Singularities.- 5 Vanishing Theorems.- 6 Base Point Freeness of Adjoint Linear Systems.- 7 Cone Theorem.- 8 Contraction Theorem.- 9 Flip.- 10 Cone Theorem Revisited.- 11 Logarithmic Mori Program.- 12 Birational Relation among Minimal Models.- 13 Birational Relation Among Mori Fiber Spaces.- 14 Birational Geometry of Tonic Varieties.- References.