scholarly journals On the Minimal Model Theory for DLT Pairs of Numerical Log Kodaira Dimension Zero

2011 ◽  
Vol 18 (5) ◽  
pp. 991-1000 ◽  
Author(s):  
Yoshinori Gongyo
Keyword(s):  
Model Theory ◽  
Minimal Model ◽  
Kodaira Dimension ◽  
Dimension Zero

scholarly journals Reduction maps and minimal model theory

2012 ◽  
Vol 149 (2) ◽  
pp. 295-308 ◽  
Author(s):  
Yoshinori Gongyo ◽  
Brian Lehmann
Keyword(s):  
Model Theory ◽  
Minimal Model ◽  
Model Program ◽  
Minimal Model Program ◽  
Birational Model ◽  
Terminal Pair

AbstractWe use reduction maps to study the minimal model program. Our main result is that the existence of a good minimal model for a Kawamata log terminal pair (X,Δ) can be detected on a birational model of the base of the (KX+Δ)-trivial reduction map. We then interpret the main conjectures of the minimal model program as a natural statement about the existence of curves on X.

scholarly journals Morphisms of projective varieties from the viewpoint of minimal model theory

2003 ◽  
Vol 413 ◽  
pp. 1-72 ◽  
Author(s):  
Marco Andreatta ◽  
Massimiliano Mella
Keyword(s):  
Model Theory ◽  
Minimal Model ◽  
Projective Varieties

scholarly journals On existence of log minimal models

2010 ◽  
Vol 146 (4) ◽  
pp. 919-928 ◽  
Author(s):  
Caucher Birkar
Keyword(s):  
Minimal Model ◽  
Kodaira Dimension ◽  
Reduction Theorem ◽  
Model Program ◽  
Minimal Models ◽  
Minimal Model Program ◽  
Log Minimal Model Program ◽  
Negative Kodaira Dimension

AbstractIn this paper, we prove that the log minimal model program in dimension d−1 implies the existence of log minimal models for effective lc pairs (e.g. of non-negative Kodaira dimension) in dimension d. In fact, we prove that the same conclusion follows from a weaker assumption, namely, the log minimal model program with scaling in dimension d−1. This enables us to prove that effective lc pairs in dimension five have log minimal models. We also give new proofs of the existence of log minimal models for effective lc pairs in dimension four and of the Shokurov reduction theorem.

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