scholarly journals Remarks on special kinds of the relative log minimal model program

2018 ◽  
Vol 160 (3-4) ◽  
pp. 285-314 ◽  
Author(s):  
Kenta Hashizume
Keyword(s):  
Minimal Model ◽  
Model Program ◽  
Minimal Model Program ◽  
Log Minimal Model Program

scholarly journals Modular compactifications of the space of pointed elliptic curves II

2011 ◽  
Vol 147 (6) ◽  
pp. 1843-1884 ◽  
Author(s):  
David Ishii Smyth
Keyword(s):  
Elliptic Curves ◽  
Moduli Spaces ◽  
Minimal Model ◽  
Model Program ◽  
Minimal Model Program ◽  
Stable Curves ◽  
Log Minimal Model Program

AbstractWe prove that the moduli spaces of n-pointed m-stable curves introduced in our previous paper have projective coarse moduli. We use the resulting spaces to run an analogue of Hassett’s log minimal model program for $\overline {M}_{1,n}$.

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.

scholarly journals Smooth projective horospherical varieties of Picard group $\mathbb{Z}^2$

2020 ◽  
Vol Volume 4 ◽  
Author(s):  
Boris Pasquier
Keyword(s):  
Minimal Model ◽  
Picard Group ◽  
Model Program ◽  
Minimal Model Program ◽  
Log Minimal Model Program ◽  
International Audience

International audience We classify all smooth projective horospherical varieties of Picard group $\mathbb{Z}^2$ and we give a first description of their geometry via the Log Minimal Model Program.

Geography of log models via asymptotic base loci

2014 ◽  
Vol 25 (09) ◽  
pp. 1450089
Author(s):  
Sung Rak Choi
Keyword(s):  
Minimal Model ◽  
Partial Answer ◽  
Model Program ◽  
Minimal Model Program ◽  
Structure Theorems ◽  
Log Minimal Model Program ◽  
Base Loci

The geography of log models refers to the decomposition of the set of effective adjoint divisors into the polytopes defined by the resulting models obtained by the log minimal model program. We will describe the geography of log models in terms of the asymptotic base loci and Zariski decompositions of adjoint divisors. As an application, we prove some structure theorems on partially ample cones, thereby giving a partial answer to a question of B. Totaro.

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