Introduction to the Mori Program

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 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