Related papers: IMPANGA lecture notes on log canonical thresholds
We investigate the variation of log canonical thresholds in (graded) linear systems. For toric log Fano varieties, we give a sharp lower bound for log canonical thresholds of the anticanonical members in terms of the global minimal log…
In terms of log canonical threshold, we characterize plurisubharmonic functions with logarithmic asymptotical behaviour.
We prove that the log canonical thresholds of a large class of binomial ideals, such as complete intersection binomial ideals and the defining ideals of space monomial curves, are computable by linear programming.
We generalize the formula for the log canonical threshold(LCT) of plane curves over the complex numbers to arbitrary characteristics. Our proof relies purely on valuation theory, instead of on the theory of $D$-modules.
The log canonical thresholds of irreducible quasi-ordinary hypersurface singularities are computed, using an explicit list of pole candidates for the motivic zeta function found by the last two authors.
We study log canonical thresholds on quartic threefolds, quintic fourfolds, and double spaces. As an application, we show that they have a Kaehler-Einstein metric if they are general.
We present a procedure for computing the log-canonical threshold of an arbitrary ideal generated by binomials and monomials. The computation of the log canonical threshold is reduced to the problem of computing the minimum of a function,…
We give an explicit formula for the log-canonical threshold of a reduced germ of plane curve. The formula depends only on the first two maximal contact values of the branches and their intersection multiplicities. We also improve the two…
We compute log canonical thresholds of reduced plane curves of degree $d$ at points of multiplicity $d-1$. As a consequence, we describe all possible values of log canonical threshold that are less than $2/(d-1)$ for reduced plane curves of…
In this paper, we show the log canonical threshold values of the surfaces which has du Val type singularities.These surfaces can be interpreted as statistical or machine learning models. The results of $A_n, D_n, E_6, E_7$ and $E_8$ are…
We show that log canonical thresholds satisfy the ACC
In this paper, we define potential log canonical threshold and prove that the set of those thresholds satisfies the ascending chain condition (ACC). We also consider collections of sequences of Fano type varieties and we study their basic…
We prove the ascending chain condition for log canonical thresholds of bounded coregularity.
We express the Segre class of a monomial scheme in projective space in terms of log canonical thresholds of associated ideals. Explicit instances of the relation amount to identities involving the classical polygamma functions.
We present the elementary properties of log canonical centers of log varieties.
We show that log canonical thresholds of fixed dimension are standardized. More precisely, we show that any sequence of log canonical thresholds in fixed dimension $d$ accumulates in a way which is i) either similar to how standard and…
We compute global log canonical thresholds of some smooth Fano threefolds.
We show that the log canonical threshold of a generic determinantal variety and its generic link are the same.
We give new examples of terminal and log canonical singularities.
We show that log canonical thresholds for complex analytic spaces satisfy the ACC.