Related papers: Singular del Pezzo surfaces that are equivariant c…

We introduce the notion of quasi-$F$-splitting in mixed characteristic and study Kodaira-type vanishing on quasi-$F$-splitting varieties. As an application, we prove a Kodaira-type vanishing on lifts of rational double point (RDP) del Pezzo…

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…

Inspired by the recent progress by Coates-Corti-Kasprzyk et al. on Mirror Symmetry for del Pezzo surfaces, we show that for any positive integer k the deformation families of del Pezzo surfaces with a single 1/k(1,1) singularity (and no…

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 describe the GIT compactification for the moduli space of smooth quintic surfaces in projective space. In particular, we show that a normal quintic surface with at worst an isolated double point or a minimal elliptic singularity is…

In this paper, we classify del Pezzo foliations on projective manifolds of rank at least 3 and with log canonical singularities in the sense of McQuillan.

We study the syzygetic structure of projections of del Pezzo surfaces in order to construct singular Calabi-Yau threefolds. By smoothing those threefolds, we obtain new examples of Calabi-Yau threefolds with Picard group of rank 1. We also…

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…

Given a degree one del Pezzo surface with canonical singularities, the linear series generated by twice the anti-canonical divisor exhibits the surface as the double cover of the quadric cone branched along a sextic curve. It is natural to…

We show that simultaneous log resolutions of simply elliptic singularities can be constructed inside suitable stacks of principal bundles over elliptic curves. In particular, we give a direct geometrical construction of del Pezzo surfaces…

We prove that singular minimal surfaces with constant Gauss curvature are planes, spheres and cylindrical surfaces. We also classify all singular minimal surfaces with a constant principal curvature and singular minimal surfaces with…

We use classification of non-symplectic automorphisms of K3 surfaces to obtain a partial classification of log del Pezzo surfaces of index three. We can classify those with "Multiple Smooth Divisor Property", whose definition we will give.…

We exhibit new examples of rational cubic fourfolds, parametrized by a countably infinite union of codimension-two subvarieties in the moduli space. Our examples are fibered in sextic del Pezzo surfaces over the projective plane; they are…

The goal of this paper is to construct a compactification of the moduli space of degree $d \ge 5$ surfaces in $\mathbb{P}^3$, i.e. a parameter space whose interior points correspond to (equivalence classes of) smooth surfaces in…

We investigate torsion exceptional sheaves on a weak del Pezzo surface of degree greater than two whose anticanonical model has at most $A_n$-singularities. We show that every torsion exceptional sheaf can be obtained from a line bundle on…

For a regular del Pezzo surface $X$, we prove that $|-12K_X|$ is very ample. Furthermore, we also give an explicit upper bound for the volume $K_X^2$ which depends only on $[k : k^p]$ for the base field $k$. As a consequence, we obtain the…

In these notes, we consider self-maps of degree > 1 on a weak del Pezzo surface X of degree < 8. We show that there are exactly 12 such X, modulo isomorphism. In particular, K_X^2 > 2, and if X has one self-map of degree > 1 then for every…

Let X be a K3 surface with an involution g which has non-empty fixed locus X^g and acts non-trivially on a non-zero holomorphic 2-form. We shall construct all such pairs (X, g) in a canonical way, from some better known double coverings of…

We study intersections of exceptional curves on del Pezzo surfaces of degree 1, motivated by questions in arithmetic geometry. Outside characteristics 2 and 3, at most 10 exceptional curves can intersect in a point. We classify the…

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.