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Foundations of the Minimal Model Program by Osamu Fujino (2017, Trade Paperback)
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About this product
Product Identifiers
PublisherMathematical Society of Japan
ISBN-104864970459
ISBN-139784864970457
eBay Product ID (ePID)240979251
Product Key Features
SubjectGeometry / Algebraic
Publication Year2017
LanguageEnglish
Publication NameFoundations of the Minimal Model Program
TypeTextbook
AuthorOsamu Fujino
Subject AreaMathematics
FormatTrade Paperback
Additional Product Features
Intended AudienceTrade
SynopsisAround 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 Koll r'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
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