Related papers: Del Pezzo surfaces with many symmetries
For split smooth Del Pezzo surfaces, we analyse the structure of the effective cone and prove a recursive formula for the value of alpha, appearing in the leading constant as predicted by Peyre of Manin's conjecture on the number of…
We prove that $\delta$-invariants of smooth cubic surfaces are at least $\frac{6}{5}$.
We classify smooth surfaces whose higher cohomologies of i-forms for all i vanish. We show that if such a surface is not affine, then it has essentially two possibilities.
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…
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…
In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree 1.
We study del Pezzo varieties, higher-dimensional analogues of del Pezzo surfaces. In particular, we introduce ADE classification of del Pezzo varieties, show that in type A the dimension of non-conical del Pezzo varieties is bounded by $12…
We show that smooth quintic del Pezzo threefolds over arbitrary base schemes are classified by non-degenerate ternary symmetric bilinear forms. Then we describe the automorphism group schemes, the Hilbert schemes of lines and the orbit…
In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree $\ge 4$.
We classify codimension 2 well-formed and quasi-smooth weighted complete intersection del Pezzo surfaces.
We give examples of K-unstable singular del Pezzo surfaces which are weighted hypersurfaces with index 2.
We give an explicit counter-example to a conjecture of Kyusik Hong and Joonyeong Won about $\alpha$-invariants of polarized smooth del Pezzo surfaces of degree one.
In this article, we compute $\delta$-invariant of Du Val del Pezzo surfaces of degree $3$.
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…
We classify del Pezzo surfaces with Picard number is equal to one and with four log terminal singular points.
We determine which singular del Pezzo surfaces are equivariant compactifications of G_a^2, to assist with proofs of Manin's conjecture for such surfaces. Additionally, we give an example of a singular quartic del Pezzo surface that is an…
We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model…
This paper focuses on the classification of all toric log Del Pezzo surfaces with exactly one singularity up to isomorphism, and on the description of how they are embedded as intersections of finitely many quadrics into suitable projective…
We classify geometrically integral regular del Pezzo surfaces which are not geometrically normal over imperfect fields of positive characteristic. Based on this classification, we show that a three-dimensional terminal del Pezzo fibration…
In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree 2.