Related papers: Classification of log Enriques surfaces with delta…

We classify all primitive embeddings of the lattice of numerical equivalence classes of divisors of an Enriques surface with the intersection form multiplied by 2 into an even unimodular hyperbolic lattice of rank 26. These embeddings have…

A nodal Enriques surface can have at most 8 nodes. We give an explicit description of Enriques surfaces with 8 nodes, showing that they are quotients of products of elliptic curves by a group isomorphic to $\Z_2^2$ or to $\Z_2^3$ acting…

In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree 2.

Log del Pezzo surfaces play the role of the opposite of surfaces of general type. We will completely classify all the log del Pezzo surfaces of rank 2 and Cartier index 3 with a unique singularity.

We classify del Pezzo surfaces with Picard number is equal to one and with four log terminal singular points.

We classify minimal surfaces $S$ with $p_g=q=2$ and $K_S^2=5$ or $6$.

Given d in IN, we prove that any polarized Enriques surface (over any field of characteristic different from 2 or with a smooth K3 cover) of degree greater than 12d^2 contains at most 12 rational curves of degree at most d. For d>2 we…

We give a notion of ordinary Enriques surfaces and their canonical lifts in any positive characteristic, and we prove Torelli-type results for this class of Enriques surfaces.

This is an expanded version of our work [AN88], 1988, in Russian. We classify del Pezzo surfaces over C with log terminal singularities of index \le 2. By classification, we understand a description of the intersection graph of all…

In the present paper we describe the K3 surfaces admitting order 11 automorphisms and apply this to classify log Enriques surfaces of global index 11.

We classify Enriques surfaces with smooth K3 cover and finite automorphism group in arbitrary positive characteristic. The classification is the same as over the complex numbers except that some types are missing in small characteristics.…

We consider log del Pezzo surfaces coming with a non-trivial torus action. Such a surface is 1/k-log canonical if it allows a resolution of singularities with discrepanies all greater or equal to 1/k-1. We provide a concrete classification…

We prove that $\delta$-invariants of smooth cubic surfaces are at least $\frac{6}{5}$.

We prove that two Enriques surfaces defined over an algebraically closed field of characteristic different from $2$ are isomorphic if their Kuznetsov components are equivalent. This improves and completes our previous result joint with Nuer…

We describe a geometric, stable pair compactification of the moduli space of Enriques surfaces with a numerical polarization of degree 2, and identify it with a semitoroidal compactification of the period space.

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 contemplate the range of convex Fujita numbers for minimal smooth projective surfaces according to their position in the Kodaira-Enriques classification.

Let $\bar{Y}$ be a normal surface that is the canonical $\mu_2$- or $\alpha_2$-covering of a classical or supersingular Enriques surface in characteristic $2$. We determine all possible configurations of singularities on $\bar{Y}$, and for…

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.

This is a brief introduction to the theory of Enriques surfaces over arbitrary algebraically closed fields. Some new results about automorphism groups of Enriques surfaces are also included.