scholarly journals Shokurov's ACC conjecture for log canonical thresholds on smooth varieties

2010 ◽  
Vol 152 (1) ◽  
pp. 93-114 ◽  
Author(s):  
Tommaso De Fernex ◽  
Lawrence Ein ◽  
Mircea Mustaţă
Keyword(s):  
Log Canonical

scholarly journals On minimal log discrepancies and kollár components

2021 ◽  
pp. 1-20
Author(s):  
Joaquín Moraga
Keyword(s):  
Blow Up ◽  
Chain Condition ◽  
Fano Varieties ◽  
Finite Sets ◽  
Fixed Dimension ◽  
Log Canonical ◽  
Finite Set ◽  
Canonical Singularities ◽  
Ascending Chain Condition

Abstract In this article, we prove a local implication of boundedness of Fano varieties. More precisely, we prove that $d$ -dimensional $a$ -log canonical singularities with standard coefficients, which admit an $\epsilon$ -plt blow-up, have minimal log discrepancies belonging to a finite set which only depends on $d,\,a$ and $\epsilon$ . This result gives a natural geometric stratification of the possible mld's in a fixed dimension by finite sets. As an application, we prove the ascending chain condition for minimal log discrepancies of exceptional singularities. We also introduce an invariant for klt singularities related to the total discrepancy of Kollár components.

scholarly journals Learning Coefficient of Vandermonde Matrix-Type Singularities in Model Selection

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 561
Author(s):  
Miki Aoyagi
Keyword(s):  
Model Selection ◽  
Information Criteria ◽  
Learning Systems ◽  
Vandermonde Matrix ◽  
Selection Methods ◽  
Learning Models ◽  
Matrix Type ◽  
Log Canonical Threshold ◽  
Log Canonical ◽  
Blowing Up

In recent years, selecting appropriate learning models has become more important with the increased need to analyze learning systems, and many model selection methods have been developed. The learning coefficient in Bayesian estimation, which serves to measure the learning efficiency in singular learning models, has an important role in several information criteria. The learning coefficient in regular models is known as the dimension of the parameter space over two, while that in singular models is smaller and varies in learning models. The learning coefficient is known mathematically as the log canonical threshold. In this paper, we provide a new rational blowing-up method for obtaining these coefficients. In the application to Vandermonde matrix-type singularities, we show the efficiency of such methods.

scholarly journals On isolated log canonical centers

2014 ◽  
Vol 54 (3) ◽  
pp. 497-505
Author(s):  
Chih-Chi Chou
Keyword(s):  
Log Canonical
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