Related papers: Weighted complete intersection del Pezzo surfaces

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 classify smooth Fano weighted complete intersections of large codimension.

We prove that a smooth well formed Picard rank one Fano complete intersection of dimension at least 2 in a toric variety is a weighted complete intersection.

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

We study del Pezzo surfaces that are quasismooth and well-formed weighted hypersurfaces. In particular, we find all such surfaces whose alpha-invariant of Tian is greater than 2/3.

We find normal forms for del Pezzo surfaces of degree $2$ over algebraically closed fields of characteristic $2$. For each normal form, we describe the structure of the group of automorphisms of the surface. In particular, we classify all…

We classify the automorphism groups of del Pezzo surfaces of degrees one and two over an algebraically closed field of characteristic two. This finishes the classification of automorphism groups of del Pezzo surfaces in all characteristics.

In an algebro-geometric way, we completely determine whether smooth del Pezzo surfaces are K-(semi)stable or not.

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

Hirschfeld classified split del Pezzo surfaces of degree at least three whose points are all contained on the lines in the surface. We continue his work and begin the classification of split degree two del Pezzo surfaces over finite fields…

We prove that a smooth well formed Fano weighted complete intersection of codimension 2 has a nef partition. We discuss applications of this fact to Mirror Symmetry. In particular we list all nef partitions for smooth well formed Fano…

We completely classify K-stability of log del Pezzo hypersurfaces with index 2.

We provide explicit graded constructions of orbifold del Pezzo surfaces with rigid orbifold points of type $\left\{k_i\times\frac{1}{r_i}(1,a_i): 3\le r_i \le 10,k_i \in \ZZ_{\ge 0}\right\}$; as well-formed and quasismooth varieties…

We prove two conjectures on weighted complete intersections and give the complete classification of threefold weighted complete intersections in weighted projective space that are canonically or anticanonically embedded.

We investigate the density of integer solutions to certain binary inhomogeneous quadratic congruences and use this information to detect almost primes on a singular del Pezzo surface of degree 6.

Previous work of the authors showed that every quartic del Pezzo surface over a number field has index dividing $2$ (i.e., has a closed point of degree $2$ modulo $4$),, and asked whether such surfaces always have a closed point of degree…

We address weak approximation for certain del Pezzo surfaces defined over the function field of a curve. We study the rational connectivity of the smooth locus of degree two del Pezzo surfaces with two A1 singularities in order to prove…

We prove the following: (a) Let X be a smooth, codimension two subvariety of P6. If X lies on a hyperquintic or if deg(X)<74, then X is a complete intersection. (b) Let X be a smooth, subcanonical threefold in P5. If X lies on a…

We show that smooth well formed weighted complete intersections have finite automorphism groups, with several obvious exceptions.

Any smooth projective variety contains many complete intersection subvarieties with ample cotangent bundles, of each dimension up to half its own dimension.