Related papers: On extra-special Enriques surfaces

We give conceptual proofs of some results on the automorphism group of an Enriques surface X, for which only computational proofs have been available. Namely, there is an obvious upper bound on the image of Aut(X) in the isometry group of…

We conjecture an explicit formula for the $K$-theoretically refined Vafa-Witten invariants of the Enriques surface. By a wall-crossing argument the conjecture is equivalent to a new conjectural formula for the K-theoretically refined…

We work out normal forms for quasi-elliptic Enriques surfaces and give several applications. These include torsors and numerically trivial automorphisms, but our main application is the completion of the classification of Enriques surfaces…

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 show that every classical Enriques surface containing a smooth rational curve is a Reye congruence.

We prove the rationality of the coarse moduli spaces of Coble surfaces and of nodal Enriques surfaces over the field of complex numbers.

We classify all non-extendable 3-sequences of half-fibers on Enriques surfaces. If the characteristic is different from 2, we prove in particular that every Enriques surface admits a 4-sequence, which implies that every Enriques surface is…

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…

We study the arithmetic of Enriques surfaces whose universal covers are singular K3 surfaces. If a singular K3 surface X has discriminant d, then it has a model over the ring class field d. Our main theorem is that the same holds true for…

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 Enriques surfaces of zero entropy, or, equivalently, Enriques surfaces with a virtually abelian automorphism group.

We verify that elliptic K3 surfaces and algebraic groups have many rational points over function fields, i.e., they are geometrically special in the sense of Javanpeykar-Rousseau. We also show that under additional assumptions, this…

We show that there is no family of Enriques surfaces over the ring of integers. This extends non-existence results of Minkowski for families of finite \'etale schemes, of Tate and Ogg for families of elliptic curves, and of Fontaine and…

Let $X$ be an Enriques surface defined over a number field $K$. Then there exists a finite extension $K'/K$ such that the set of $K'$-rational points of $X$ is Zariski dense.

We classify Enriques involutions on a K3 surface, up to conjugation in the automorphism group, in terms of lattice theory. We enumerate such involutions on singular K3 surfaces with transcendental lattice of discriminant smaller than or…

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.

We give a proof of the Morrison-Kawamata cone conjecture for Enriques surfaces independent of their characteristic. It is based on the analysis of certain generically finite morphisms of degree two.

This paper proposes a new geometric construction of Enriques surfaces. Its starting point are K3 surfaces with jacobian elliptic fibration which arise from rational elliptic surfaces by a quadratic base change. The Enriques surfaces…

We run an iteration argument due to Pramanik and Seeger, to provide a proof of sharp decoupling inequalities for conical surfaces and for $k$-cones. These are extensions of results \L aba and Pramanik to sharp exponents.

We prove that, for an Enriques surface in odd characteristic, the automorphism group is finitely generated and it acts on the effective nef cone with a rational polyhedral fundamental domain. We also construct a smooth projective surface in…