Related papers: Log canonical thresholds of del Pezzo surfaces
Toric log del Pezzo surfaces correspond to convex lattice polygons containing the origin in their interior and having only primitive vertices. An upper bound on the volume and on the number of boundary lattice points of these polygons is…
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 classify smooth del Pezzo surfaces whose alpha-invariant of Tian is bigger than one.
Log del Pezzo surfaces play the role of the opposite of surfaces of general type. We will completely classify all the log del Pezzo surfaces of rank 2 and Cartier index 3 with a unique singularity.
Del Pezzo surfaces over C with log terminal singularities of index \le 2 were classified by Alekseev and Nikulin. In this paper, for each of these surfaces, we find an appropriate morphism to projective space. These morphisms enable us to…
We construct algebraic geometric codes from del Pezzo surfaces and focus on the ones having Picard rank one and the codes associated to the anticanonical class. We give explicit constructions of del Pezzo surfaces of degree 4, 5 and 6,…
We classify all log del Pezzo surfaces of Picard number one defined over algebraically closed fields of characteristic different from two and three. We also discuss some consequences of the classification. For example, we show that log del…
We construct the first examples of regular del Pezzo surfaces for which the irregularity (i.e. the dimension of the first cohomology group of the structure sheaf) is nonzero. We also find a restriction on the integer pairs that are possible…
We continue our quest for real enumerative invariants not sensitive to changing the real structure and extend the construction we uncovered previously for counting curves of anti-canonical degree $\leqslant 2$ on del Pezzo surfaces with…
We show that log canonical thresholds satisfy the ACC
The global log canonical threshold (or Tian's alpha-invariant) plays an important role in the geometry of Fano varieties. Tian showed that Fano manifolds with big alpha-invariant can be equipped with a Kahler-Einstein metric. In recent…
Working over a perfect field, I classify normal del Pezzo surfaces with base number one that contain a nonrational singularity. They form a huge infinite hierarchy; contractions of ruled surfaces lie on top of it. Descending the hierarchy…
Toric log Del Pezzo surfaces with Picard number 1 have been completely classified whenever their index is $\le 2$: In this paper we extend the classification for those having index 3: We prove that, up to isomorphism, there are exactly 18…
In this note, we compute the Poisson cohomology groups for any Poisson Del Pezzo surface.
This is the first article in a series aimed at classifying normal del Pezzo surfaces of Picard rank one over algebraically closed fields of arbitrary characteristic up to an isomorphism. Our guiding invariant is the height of a del Pezzo…
We introduce the notion of generalized MR log canonical surfaces and establish the minimal model theory for generalized MR log canonical surfaces in full generality.
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.
We show that the log canonical threshold of a generic determinantal variety and its generic link are the same.
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 study log canonical models of foliated surfaces of general type. In particular, we show that log canonical models of general type and their minimal partial du Val resolutions are bounded. Moreover, we show the valuative criteria of…