Related papers: Complexity of del Pezzo surfaces with du Val singu…

In this article, we compute $\delta$-invariant of Du Val del Pezzo surfaces of degree $3$.

In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree 1.

We classify del Pezzo surfaces with Du Val singularities that have infinite automorphism groups, and describe the connected components of their automorphisms groups.

In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree 2.

We compute the coregularity of del Pezzo surfaces with du Val singularities. To this aim, we study the relation between del Pezzo surfaces of degree $1$ and elliptic fibrations. It turns out that del Pezzo surfaces with positive…

In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree $\ge 4$.

We study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm how to classify all of them.

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…

In this note, we compute the Poisson cohomology groups for any Poisson Del Pezzo surface.

We consider del Pezzo surfaces $X$ with du Val singularities. Assume that $X$ has a $-K_X$-polar cylinder and $\deg X=1$. Let $H$ be an ample divisor. We'll prove that $X$ has a $H$-polar cylinder.

In this paper we consider the classification of singularities (Du Val) and real structures (Wall) of weak Del Pezzo surfaces from an algorithmic point of view. It is well known that the singularities of weak Del Pezzo surfaces correspond to…

In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type…

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

Let $S$ be a del Pezzo surface with at worse Du Val singularities of degree $\ge 3$. We construct an $H$-polar cylinder for any ample $\mathbb{Q}$-divisor $H$ on $S$.

We give examples of K-unstable singular del Pezzo surfaces which are weighted hypersurfaces with index 2.

Let $S$ be a del Pezzo surface with at worst Du Val singularities of degree $2$ such that $S$ admits an $(-K_S)$-polar cylinder. In this article, we construct an $H$-polar cylinder for any ample $\mathbb{Q}$-divisor $H$ on $S$.

We present a description for the automorphism groups of Du Val del Pezzo surfaces whose automorphism groups are infinite.

We classify smooth del Pezzo surfaces whose alpha-invariant of Tian is bigger than one.

We classify all the del Pezzo surfaces with $\frac{1}{3}(1,1)$- and $\frac{1}{4}(1,1)$-singularities having no floating $(-1)$-curves into 39 types.

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