Related papers: Weighted complete intersection del Pezzo surfaces
On del Pezzo surfaces, we study effective ample $\mathbb{R}$-divisors such that the complements of their supports are isomorphic to $\mathbb{A}^1$-bundles over smooth affine curves.
In this article, we obtain an upper bound for the number of integral points on the del Pezzo surfaces of degree two.
We present new constructions of Kaehler metrics with constant scalar curvature on complex surfaces, in particular on certain del Pezzo surfaces. Some higher dimensional examples are provided as well.
We prove that if a smooth variety with non-positive canonical class can be embedded into a weighted projective space of dimension $n$ as a well formed complete intersection and it is not an intersection with a linear cone therein, then the…
We survey some of the recent works on the geometry of del Pezzo surfaces over imperfect fields, with applications to 3-dimensional del Pezzo fibrations in positive characteristic. We place particular emphasis on cases where the general…
We calculate intersection forms of all 4-dimensional almost-flat manifolds
We explain a classical construction of a del Pezzo surface of degree d = 4 or 5 as a smooth order two congruence of lines in 3-space whose focal surface is a quartic surface $X_{20-d}$ with 20-d ordinary double points. We also show that…
In the literature there are two definitions of well formed varieties in weighted projective spaces. According to the first one, well formed variety is the one whose intersection with the singular locus of the ambient weighted projective…
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 complete the classification of automorphism groups of del Pezzo surfaces over algebraically closed fields of odd positive characteristic.
The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.
We give a classification of toric log del Pezzo surfaces with two or three singular points.
We show that on quasi-smooth weighted complete intersections of codimension at most 3, any ample Cartier divisor $H$ such that $H-K_X$ is ample admits a nontrivial global section. This is done by proving a generalisation of a numerical…
We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of…
It is known that any Mori fiber space birational to a minimal smooth del Pezzo surface $S$ of degree $4$ is either a del Pezzo surface of degree $4$ itself, or a smooth cubic surface with a structure of a relatively minimal conic bundle. We…
We classify complete biharmonic surfaces with parallel mean curvature vector field and non-negative Gaussian curvature in complex space forms.
In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree 2.
We describe a normal form for a smooth intersection of two quadrics in even-dimensional projective space over an arbitrary field of characteristic 2. We use this to obtain a description of the automorphism group of such a variety. As an…
Real, complex, and tropical algebraic geometry join forces in a new branch of mathematical physics called positive geometry. We develop the positive geometry of del Pezzo surfaces and their moduli spaces, viewed as very affine varieties.…
We obtain sharp estimates on the connectivity of complex affine hypersurfaces in terms of the decomposition of the defining equation as a sum of weighted homogeneous components relative to some weight system.