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Minimal model program

About: Minimal model program is a research topic. Over the lifetime, 476 publications have been published within this topic receiving 15197 citations.


Papers
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Book
01 Jan 1998
TL;DR: In this paper, the authors introduce the minimal model program and the canonical class of rational curves, and present the singularities of the model program, as well as three dimensional flops.
Abstract: 1. Rational curves and the canonical class 2. Introduction to minimal model program 3. Cone theorems 4. Surface singularities 5. Singularities of the minimal model program 6. Three dimensional flops 7. Semi-stable minimal models.

1,754 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that pl-flips exist in dimension n − 1, assuming finite generation in dimension N − 1 and assuming that pl flips exist in all dimensions.
Abstract: Assuming finite generation in dimension n − 1, we prove that pl-flips exist in dimension n.

1,612 citations

MonographDOI
01 Feb 2013
TL;DR: In this paper, the authors present a survey of Canonical and log canonical singularities and their application in the context of finite equivalence relations, including semi-log-canonical pairs and the Du Bois property.
Abstract: Preface Introduction 1. Preliminaries 2. Canonical and log canonical singularities 3. Examples 4. Adjunction and residues 5. Semi-log-canonical pairs 6. Du Bois property 7. Log centers and depth 8. Survey of further results and applications 9. Finite equivalence relations 10. Appendices References Index.

739 citations

Book
01 Jan 2001
TL;DR: A good introduction to algebraic geometry can be found in this paper, where the authors provide an easily accessible introduction to the subject and provide a mostly self-contained introduction to graduate students and researchers.
Abstract: Higher-dimensional algebraic geometry studies the classification theory of algebraic varieties. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The author?s goal is to provide an easily accessible introduction to the subject. The book covers preparatory and standard definitions and results, moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Mori?s minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction to graduate students and researchers.

625 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202123
202027
201926
201837
201742
201634