Introduction to the Mori Program
By: by Kenji Matsuki
Series: Universitext; Universitext
Publisher: Springer New York
Published: 2002
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 479
ISBN-13: 9781441931252; 9781475756029
Subjects: Mathematics; Algebraic Geometry
Description: The purpose of this book is to give a comprehensible account of what is called Mori's Program, that is an approach to the following problem: classify all the projective varieties X /in P^n over C up to isomorphism. 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." 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.
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Table of contents: title: Introduction; title: Birational Geometry of Surfaces; title: Logarithmic Category; title: Overview of Mori's Program; title: Singularities; title: Vanishing Theorems; title: Base Point Freeness of Linear Systems; title: Cone Theorem; title: Contraction Theorem; title: Flip; title: Cone Theorem Revisited; title: Logarithmic Mori's Program; title: Birational Relations among Minimal Models; title: Birational Relations among Mori Fiber Spaces; title: Birational Geometry of Toric Varieties.