Reye constructions for nodal Enriques surfaces

The rationality of the moduli spaces of Coble surfaces and of nodal Enriques surfaces

The purpose of this note is to prove the rationality of the moduli spaces of Coble surfaces and of nodal Enriques surfaces over the field of complex numbers. A Coble surface is a rational surface obtained by blowing up 10 nodes of a rational plane curve of degree 6, and an Enriques surface is said to be nodal if it contains a smooth rational curve. The moduli space of nodal Enriques surfaces is...

Around real Enriques surfaces

We present a brief overview of the classiication of real Enriques surfaces completed recently and make an attempt to systemize the known clas-siication results for other special types of surfaces. Emphasis is also given to the particular tools used and to the general phenomena discovered; in particular , we prove two new congruence type prohibitions on the Euler characteristic of the real part ...

The Period Lattice for Enriques Surfaces

It is well-known that the isomorphism classes of complex Enriques surfaces are in 1-1 correspondence with a Zariski-open subset (D ? H)=? of the quotient of the Hermitian symmetric space D for O(2; 10). Here H is a totally geodesic divisor in D and ? is a certain arithmetic group. In the usual formulation of this result 5], ? is described as the isometry group of a certain integral lattice N of...

Enriques surfaces covered by Jacobian Kummer surfaces

This paper classifies Enriques surfaces whose K3-cover is a fixed Picard-general Jacobian Kummer surface. There are exactly 31 such surfaces. We describe the free involutions which give these Enriques surfaces explicitly. As a biproduct, we show that Aut(X) is generated by elements of order 2, which is an improvement of the theorem of S. Kondo.

On Automorphisms of Nodal Enriques Surfaces by F. Cossec and I. Dolgachev