Related papers: A brief introduction to Enriques surfaces
We classifiy Enriques surfaces covered by the supersingular K3 surface with the Artin invariant 1 in characteristic 2. There are exactly three types of such Enriques surfaces.
The main purpose in this paper is to study exceptional vector bundles on Enriques surfaces.
We introduce logarithmic Enriques varieties as a singular analogue of Enriques manifolds, generalizing the notion of log-Enriques surfaces introduced by Zhang. We focus mainly on the properties of the subfamily of log-Enriques varieties…
We give an explicit construction and clasification of some very special sort of Enriques surfaces in characteristic two. This proves the existence of some of the surfaces that were called ``extra-special'' by Cossec and Dolgachev in their…
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.
A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.
Using the theory of hyperkahler manifolds, we generalize the notion of Enriques surfaces to higher dimensions and construct several examples using group actions on Hilbert schemes of points or moduli spaces of stable sheaves.
Lehmer's number $\lambda_{10}$ is the smallest dynamical degree greater than $1$ that can occur for an automorphism of an algebraic surface. We show that $\lambda_{10}$ cannot be realized by automorphisms of Enriques surfaces in odd…
This is a common introduction to math.RT/0101170, math.RT/0306333, math.RT/0506043, math.RT/0601028. Compared to these references there are new results including (i) a description of a separable closure of an extension of transcendence…
We give a closed formula for the number of orbits of smooth rational curves under the automorphism group of an Enriques surface in terms of its Nikulin root invariant and its Vinberg group.
We classify the bi-canonical representations of finite automorphisms on Enriques surfaces. There are three types of non-trivial cases and examples are given explicitly by Horikawa models. In particular, finite non-semi-symplectic…
The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.
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 overview of a few selected chapters on automorphism groups of affine varieties. It includes some open questions.
This paper develops families of complex Enriques surfaces whose Brauer groups pull back identically to zero on the covering K3 surfaces. Our methods rely on isogenies with Kummer surfaces of product type. We offer both lattice theoretic and…
A very interesting problem in the classical theory of minimal surfaces consists of the classification of such surfaces under some geometrical and topological constraints. In this short paper, we give a brief summary of the known…
We show that most classes of K3 surfaces have only finitely many Enriques quotients. For supersingular K3 surfaces over fields of characteristic $p \geq 3$, we give a formula which generically yields the number of their Enriques quotients.…
In this paper we discuss the number of Enriques quotients of a fixed K3 surface. We prove the finiteness and unboundedness of the number. We also show an example of Kummer surface of product type where we can successfully classify all the…
We classify, up to some lattice-theoretic equivalence, all possible configurations of rational double points that can appear on a surface whose minimal resolution is a complex Enriques surface.
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…