Around 1980, Shigefumi Mori initiated a new theory, which is now known as the minimal model program or Mori theory, for higher-dimensional algebraic varieties. This theory has developed into a powerful tool with applications to diverse questions in algebraic geometry and related fields.One of the main purposes of this book is to establish the fundamental theorems of the minimal model program, that is, various Kodaira type vanishing theorems, the cone and contraction theorem, and so on, for quasi-log schemes. The notion of quasi-log schemes was introduced by Florin Ambro and is now indispensable for the study of semi-log canonical pairs from the cohomological point of view. By the recent developments of the minimal model program, we know that the appropriate singularities to permit on the varieties at the boundaries of moduli spaces are semi-log canonical. In order to achieve this goal, we generalize Kollar's injectivity, torsion-free, and vanishing theorems for reducible varieties by using the theory of mixed Hodge structures on cohomology with compact support. We also review many important classical Kodaira type vanishing theorems in detail and explain the basic results of the minimal model program for the reader's convenience.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

Book Information
ISBN 9784864970457
Author Osamu Fujino
Format Paperback
Page Count 289
Imprint Mathematical Society of Japan
Publisher Mathematical Society of Japan