Singularities Of The Minimal Model Program
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Singularities Of The Minimal Model Program
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Author : János Kollár
language : en
Publisher: Cambridge University Press
Release Date : 2013-02-21
Singularities Of The Minimal Model Program written by János Kollár and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-21 with Mathematics categories.
An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.
Singularities Of The Minimal Model Program
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Author : János Kollár. Sándor Kovács
language : en
Publisher:
Release Date : 2013
Singularities Of The Minimal Model Program written by János Kollár. Sándor Kovács and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Singularities Of The Minimal Model Program
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Author : János Kollár
language : en
Publisher: Cambridge University Press
Release Date : 2013-02-21
Singularities Of The Minimal Model Program written by János Kollár and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-21 with Mathematics categories.
This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.
Foundations Of The Minimal Model Program
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Author : 藤野修 (代数学)
language : en
Publisher: Mathematical Society of Japan Memoirs
Release Date : 2017-05
Foundations Of The Minimal Model Program written by 藤野修 (代数学) and has been published by Mathematical Society of Japan Memoirs this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05 with Geometry, Algebraic categories.
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 Kollár'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
Introduction To The Mori Program
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Author : Kenji Matsuki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Introduction To The Mori Program written by Kenji Matsuki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
Birational Geometry Of Algebraic Varieties
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Author : Janos Kollár
language : en
Publisher: Cambridge University Press
Release Date : 2008-02-04
Birational Geometry Of Algebraic Varieties written by Janos Kollár and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-04 with Mathematics categories.
One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.
Classification Of Higher Dimensional Algebraic Varieties
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Author : Christopher D. Hacon
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-02
Classification Of Higher Dimensional Algebraic Varieties written by Christopher D. Hacon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-02 with Mathematics categories.
Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.
Topology Of Stratified Spaces
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Author : Greg Friedman
language : en
Publisher: Cambridge University Press
Release Date : 2011-03-28
Topology Of Stratified Spaces written by Greg Friedman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-28 with Mathematics categories.
This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.
Toric Varieties
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Author : David A. Cox
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Toric Varieties written by David A. Cox and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers the standard topics in toric geometry; a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry. Other topics covered include quotient constructions, vanishing theorems, equivariant cohomology, GIT quotients, the secondary fan, and the minimal model program for toric varieties. The subject lends itself to rich examples reflected in the 134 illustrations included in the text. The book also explores connections with commutative algebra and polyhedral geometry, treating both polytopes and their unbounded cousins, polyhedra. There are appendices on the history of toric varieties and the computational tools available to investigate nontrivial examples in toric geometry. Readers of this book should be familiar with the material covered in basic graduate courses in algebra and topology, and to a somewhat lesser degree, complex analysis. In addition, the authors assume that the reader has had some previous experience with algebraic geometry at an advanced undergraduate level. The book will be a useful reference for graduate students and researchers who are interested in algebraic geometry, polyhedral geometry, and toric varieties.
Rational And Nearly Rational Varieties
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Author : János Kollár
language : en
Publisher: Cambridge University Press
Release Date : 2004-04-22
Rational And Nearly Rational Varieties written by János Kollár and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-22 with Mathematics categories.
The most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications where algebraic varieties appear in mathematics and the sciences, we see rational ones emerging as the most interesting examples. The authors have given an elementary treatment of rationality questions using a mix of classical and modern methods. Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational and nearly rational varieties at a level that will particularly suit graduate students. There are numerous examples and exercises, all of which are accompanied by fully worked out solutions, that will make this book ideal as the basis of a graduate course. It will act as a valuable reference for researchers whilst helping graduate students to reach the point where they can begin to tackle contemporary research problems.