Related papers: ACC for log canonical thresholds

We prove the abundance theorem for semi log canonical surfaces in positive characteristic.

We prove that the LMMP works for projective threefolds over function fields of characteristic $p>5$ when the canonical divisor is not pseudo-effective. In the process we show that ACC for log canonical thresholds holds in complete…

It is shown that the log-canonical threshold of a curve with an isolated singularity is computed by the term ideal of the curve in a suitable system of local parameters at the singularity. The proof uses the Enriques diagram of the…

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…

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 show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.

Let $X$ be a smooth hypersurface of degree $n\geq 3$ in $\mathbb{P}^n$. We prove that the log canonical threshold of $H\in|-K_X|$ is at least $\frac{n-1}{n}$. Under the assumption of the Log minimal model program, we also prove that a…

We prove that the lengths of extremal rays of log canonical Fano surfaces with Picard number one satisfy the ascending chain condition. This confirms the 2-dimensional case of a conjecture stated by Fujino and Ishitsuka

We show that if a divisor centered over a point on a smooth surface computes a minimal log discrepancy, then the divisor also computes a log canonical threshold. To prove the result, we study the asymptotic log canonical threshold of the…

We study the set of log-canonical thresholds (or critical integrability indices) of holomorphic (resp. real analytic) function germs in $\mathbb{C}^2$ (resp. $\mathbb{R}^2$). In particular, we prove that the ascending chain condition holds,…

We prove that the only accumulation points of the set $T_3$ of all three-dimensional log canonical thresholds in the interval $[1/2,1]$ are $1/2+1/n$, where $n\in\ZZ$, $n\ge 3$.

Let $(X/Z,B+A)$ be a $\Q$-factorial dlt pair where $B,A\ge 0$ are $\Q$-divisors and $K_X+B+A\sim_\Q 0/Z$. We prove that any LMMP$/Z$ on $K_X+B$ with scaling of an ample$/Z$ divisor terminates with a good log minimal model or a Mori fibre…

The LCS locus is an essential ingredient in the proof of fundamental results of Log Minimal Model Program, such as nonvanishing and base point freeness theorems. We prove in this paper that the LCS locus of a log canonical variety has…

In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.

We prove that the class of log canonical rational singularities is closed under the basic operations of the minimal model program. We also give some supplementary results on the minimal model program for log canonical surfaces.

We show that every limit of log canonical thresholds of n-variable functions is also a log canonical threshold of an (n-1)-variable function.

Given a graded sequence of ideals (a_m) on a smooth variety $X$ having finite log canonical threshold, suppose that for every m we have a divisor E_m over X that computes the log canonical threshold of a_m, and such that the log…

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 show that the set $\mathcal{T}_{3, \mathrm{sm}}^{\mathrm{can}}$ of smooth threefold canonical thresholds coincides with $\mathcal{T}_{2, \mathrm{sm}}^{\mathrm{lc}}=\mathcal{HT}_{2}$, where $\mathcal{HT}_{2}$ is the $2$-dimensional…

In this paper we show that the global (log) canonical threshold of $d$-sheeted covers of the $M$-dimensional projective space of index 1, where $d\geqslant 4$, is equal to one for almost all families (except for a finite set). The varieties…