Related papers: Weak del Pezzo surfaces with global vector fields

In this paper we consider del Pezzo surfaces with only log terminal singularities admitting an action of a finite simple group.

We study minimal complex surfaces S of general type with q(S)=q and p_g(S)=2q-3, q>= 5. We give a complete classification in case that S has a fibration onto a curve of genus >=2. For these surfaces K^2=8\chi. In general we prove that…

The explicit computation of the field of moduli of a closed Riemann surface is, in general, a difficult task. In this paper, for each even integer $k \geq 2$, we consider a suitable $2$-real parameter family of non-hyperelliptic pseudo-real…

The Picard scheme of a smooth curve and a smooth complex variety is reduced. In this note we discuss which classes of surfaces in terms of the Enriques-Kodaira classification can have non-reduced Picard schemes and whether there are…

Let $K=k(C)$ be the function field of a curve over a field $k$ and let $X$ be a smooth, projective, separably rationally connected $K$-variety with $X(K)\neq\emptyset$. Under the assumption that $X$ admits a smooth projective model $\pi:…

We consider $(1,1)$-surfaces, namely, minimal compact complex surfaces $S$ with $p_g (S) =K_S^2=1$: for these the bicanonical map is a covering of degree $4$ of the plane $\mathbb{P}^2$. And we answer a question posed by Meng Chen, whether…

We give a classification of toric log del Pezzo surfaces with two or three singular points.

This article treats smooth weak Fano 3-folds having an extremal ray of type D. Smooth weak Fano 3-folds with an extremal ray of type D except of degree 6 are classified into 47 deformation types.

For each closed orientable surface we introduce a simplical complex with some additional structure which is a version of the complex of curves of this surface adjusted to investigation of its Torelli group. We call this complex the Torelli…

The study of the topology of real algebraic varieties dates back to the work of Harnack, Klein and Hilbert in the 19th century; in particular, the isotopy type classification of real algebraic curves in real toric surfaces is a classical…

We classify Galois actions on Picard lattices of del Pezzo surfaces of degrees 1,2, and 3 giving rise to minimal surfaces with no cohomological obstructions to stable rationality.

We construct a klt del Pezzo surface which is not globally F-split, over any algebraically closed field of positive characteristic.

A map is a cellular decomposition of a closed surface. In the framework of classifying all regular maps by their supporting surface, it is an open problem to find all closed surfaces that support no regular maps. Classification of regular…

Consider the family of smooth cubic surfaces which can be realized as threefold-branched covers of $\mathbb{P}^{2}$, with branch locus equal to a smooth cubic curve. This family is parametrized by the space $\mathcal{U}_{3}$ of smooth cubic…

Let $f(z)=z^5+az^3+bz^2+cz+d \in \Z[z]$ and let us consider a del Pezzo surface of degree one given by the equation $\cal{E}_{f}: x^2-y^3-f(z)=0$. In this note we prove that if the set of rational points on the curve $E_{a,…

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 obtain the list of automorphism groups for smooth plane sextic curves over an algebraically closed field K of characteristic p=0 or p>21. Moreover, we assign to each group a geometrically complete family over K describing its…

The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Koll\'ar-Shokurov's connectedness principle and other results relying on vanishing theorems of Kodaira type, not…

Recently, de Thanhoffer de Volcsey and Van den Bergh showed that Grothendieck groups of "noncommutative Del Pezzo surfaces" with an exceptional sequence of length 4 are isomorphic to one of three types, the third one not coming from a…

The Severi variety V_{n,d} of a smooth projective surface S is defined as the subvariety of the linear system |O_S(n)|, which parametrizes curves with d nodes. We show that, for a general surface S of degree k in P^3 and for all n>k-1,…