Empty real Enriques surfaces and Enriques-Einstein-Hitchin 4-manifolds.

Alexander Degtyarev , Viatcheslav Kharlamov (1)

1 IRMA - Institut de Recherche Mathématique Avancée

"We prove that the moduli space of empty real Enriques surfaces (and, thus, the moduli space of compact orientable $4$-dimensional Einstein manifolds whose universal covering is a $K3$-surface and $pi_1(E)=Bbb Z/2imesBbb Z/2$) is connected. The proof is based on a systematic study of real elliptic pencils and gives explicit models of all empty real Enriques surfaces. "

Mots clés: Enriques surfaces; real elliptic pencils; "Enriques surfaces; real algebraic surfaces; Einstein manifolds; real elliptic pencils"

Domaines: Géométrie algébrique [math.AG]

Alexander Degtyarev, Viatcheslav Kharlamov. Empty real Enriques surfaces and Enriques-Einstein-Hitchin 4-manifolds.. 1997. ⟨hal-00129569⟩