Related papers: ACC for log canonical thresholds

We obtain a correct generalization of Shokurov's non-vanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theorem for log canonical pairs. As a corollary,…

We characterize the ideals $I$ of $\mathcal O_n$ of finite colength whose integral closure is equal to the integral closure of an ideal generated by pure monomials. This characterization, which is motivated by an inequality proven by…

We discuss the ACC conjecture and the LSC conjecture for minimal log discrepancies of generalized pairs. We prove that some known results on these two conjectures for usual pairs are still valid for generalized pairs. We also discuss the…

It is proved that the global log canonical threshold of a Zariski general Fano complete intersection of index 1 and codimension $k$ in ${\mathbb P}^{M+k}$ is equal to one, if $M\geqslant 2k+3$ and the maximum of the degrees of defining…

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…

We prove the special termination for log canonical pairs and its generalisation in the context of generalised pairs.

We prove the normality of minimal log canonical centers on threefold pairs which residue fields are perfect of residue characteristics $p\neq 2,3 $ and $5$. We also show that the union of all log canonical centers on threefold pairs with…

In the paper we compute the global log canonical thresholds of the secondary Burniat surfaces with $K^2 = 5$. Furthermore, we establish optimal lower bounds for the log canonical thresholds of members in pluricanonical sublinear systems of…

In this paper, we show the abundance theorem for log canonical surfaces over fields of positive characteristic.

In this article, we investigate F-pure thresholds of polynomials that are homogeneous under some N-grading, and have an isolated singularity at the origin. We characterize these invariants in terms of the base p expansion of the…

We discuss a difference between the rational and the real non-vanishing conjecture for pseudo-effective log canonical divisors of log canonical pairs. We also show the log non-vanishing theorem for rationally connected varieties under…

Motivated by Shokurov's ACC Conjecture for log canonical thresholds, we propose an inductive point of view on singularities of pairs, in the case when the ambient variety is smooth. Our main result characterizes the log canonicity of a pair…

We compute a canonical circular-arc representation for a given circular-arc (CA) graph which implies solving the isomorphism and recognition problem for this class. To accomplish this we split the class of CA graphs into uniform and…

We prove a conjecture due to V.V. Shokurov on the boundedness of $\epsilon$-log canonical complements on surfaces. As an application we give a new proof to the boundedness of weak log Fano surfaces.

We prove that for each positive integer $n$ there exists a positive number $\epsilon_n$ so that $n$-dimensional toric quotient singularities satisfy the ACC for mld's on the interval $(0,\epsilon_n)$. In the course of the proof, we will…

We show the finiteness of log pluricanonical representations under the assumption of the existence of a good minimal model.

We define the "source" and the "spring" of a log canonical center and use them to solve several problems in higher-codimension adjunction. The main application is to the construction of semi log canonical pairs. Version 2: References…

We prove that every quasi-projective semi log canonical pair has a quasi-log structure with several good properties. It implies that various vanishing theorems, torsion-free theorem, and the cone and contraction theorem hold for semi log…

We prove several congruences for trinomial coefficients.

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for canonical $U$-statistics of arbitrary order $d$, extending the previously known results for $d=2$. The nasc's are expressed as growth conditions…