scholarly journals Floer cohomology, multiplicity and the log canonical threshold

2019 ◽  
Vol 23 (2) ◽  
pp. 957-1056
Author(s):  
Mark McLean
Keyword(s):  
Floer Cohomology ◽  
Log Canonical Threshold ◽  
Log Canonical

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 Canonical and log canonical thresholds of multiple projective spaces

2019 ◽  
Author(s):  
Aleksandr V. Pukhlikov
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Regularity Conditions ◽  
Large Classes ◽  
Log Canonical Threshold ◽  
Birational Rigidity ◽  
Log Canonical ◽  
Finite Set ◽  
Dimensional Projective Space ◽  
Almost All

AbstractWe show that the global (log) canonical threshold of d-sheeted covers of the M-dimensional projective space of index 1, where $$d\geqslant 4$$d⩾4, is equal to 1 for almost all families (except for a finite set). The varieties are assumed to have at most quadratic singularities, the rank of which is bounded from below, and to satisfy the regularity conditions. This implies birational rigidity of new large classes of Fano–Mori fibre spaces over a base, the dimension of which is bounded from above by a constant that depends (quadratically) on the dimension of the fibre only.

scholarly journals Log canonical threshold and diagonal ideals

2016 ◽  
Vol 145 (5) ◽  
pp. 1905-1916
Author(s):  
Carles Bivià-Ausina
Keyword(s):  
Log Canonical Threshold ◽  
Log Canonical

scholarly journals A procedure for computing the log canonical threshold of a binomial ideal

2017 ◽  
Vol 155 (1-2) ◽  
pp. 141-181
Author(s):  
R. Blanco ◽  
S. Encinas
Keyword(s):  
Log Canonical Threshold ◽  
Binomial Ideal ◽  
Log Canonical

scholarly journals Multiplicities and log canonical threshold

2004 ◽  
Vol 13 (3) ◽  
pp. 603-615 ◽  
Author(s):  
Tommaso de Fernex ◽  
Lawrence Ein ◽  
Mircea Mustaţǎ
Keyword(s):  
Log Canonical Threshold ◽  
Log Canonical

scholarly journals A sharp lower bound for the log canonical threshold

2014 ◽  
Vol 212 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Jean-Pierre Demailly ◽  
Hoàng Hiệp Phạm
Keyword(s):  
Lower Bound ◽  
Log Canonical Threshold ◽  
Log Canonical ◽  
Sharp Lower Bound

scholarly journals Extremal cases for the log canonical threshold

2015 ◽  
Vol 353 (1) ◽  
pp. 21-24 ◽  
Author(s):  
Alexander Rashkovskii
Keyword(s):  
Log Canonical Threshold ◽  
Log Canonical

scholarly journals IGUSA’S CONJECTURE FOR EXPONENTIAL SUMS: OPTIMAL ESTIMATES FOR NONRATIONAL SINGULARITIES

2019 ◽  
Vol 7 ◽  
Author(s):  
RAF CLUCKERS ◽  
MIRCEA MUSTAŢĂ ◽  
KIEN HUU NGUYEN
Keyword(s):  
Upper Bound ◽  
Exponential Sums ◽  
Log Canonical Threshold ◽  
Log Canonical ◽  
Optimal Estimates

We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa’s conjecture on exponential sums, with the log canonical threshold in the exponent of the estimates. We show that this covers optimally all situations of the conjectures for nonrational singularities by comparing the log canonical threshold with a local notion of the motivic oscillation index.

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