Related papers: Log canonical thresholds of del Pezzo surfaces

We classify all the effective anticanonical divisors on weak del Pezzo surfaces. Through this classification we obtain the smallest number among the log canonical thresholds of effective anticanonical divisors on a given Gorenstein…

The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Koll\'ar-Shokurov's connectedness principle and other results relying on vanishing theorems of Kodaira type, not…

The purpose of this article is to develop techniques for estimating basis log canonical thresholds on logarithmic surfaces. To that end, we develop new local intersection estimates that imply log canonicity. Our main motivation and…

We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$. As a corollary we obtain the existence of orbifold K\"ahler--Einstein metrics…

We compute global log canonical thresholds of some smooth Fano threefolds.

In this paper we study the problem of existence of orbifold Kaehler-Einstein metrics on del Pezzo surfaces of degree 1 with Du Val singular points. Moreover we compute global log canonical thresholds of del Pezzo surfaces of degree 1 with…

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.

Let $S$ be a minimal surface of general type with $p_g(S)=2$ and $K^2_S=1$, so called by a minimal $(1,2)$-surface. Then we obtain that the global log canonical threshold of the surface $S$ via $K_S$ is greater than equal to $\frac{1}{2}$.…

We classify del Pezzo surfaces of Picard number one with log canonical singularities admitting Q-Gorenstein smoothings.

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 give a classification of toric log del Pezzo surfaces with two or three singular points.

There are several variations of the definition of log del Pezzo pairs in the literature. We define their suitable smooth models, and we show that they are the same. In particular, we obtain a characterization of smooth log del Pezzo pairs…

We give an optimal upper bound for the anti-canonical volume of an $\epsilon$-lc weak log del Pezzo surface. Moreover, we consider the relation between the bound of the volume and the Picard number of the minimal resolution of the surface.…

We consider log del Pezzo surfaces coming with a non-trivial torus action. Such a surface is 1/k-log canonical if it allows a resolution of singularities with discrepanies all greater or equal to 1/k-1. We provide a concrete classification…

We classify del Pezzo surfaces with Picard number is equal to one and with four log terminal singular points.

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 give upper bounds for the number of rational points of bounded anti-canonical height on del Pezzo surfaces of degree at most five over any global field whose characteristic is not equal to two or three. For number fields these results…

The exceptional log Del Pezzo surfaces with delta=1 are classified.

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…

We study global log canonical thresholds of cubic surfaces with canonical singularities, and we prove the existence of a Kahler-Einstein metric on two singular cubic surfaces.