The Double Cover of an Enriques Surface

Abstract: Every Enriques surface possesses a canonically defined flat double cover. In characteristic not equal to 2, this cover is etale and the covering surface is a K3 surface. Projective models of the K3 surfaces that arise this way have been obtained by Cossec and Verra (and, of course, have been 'known' to Enriques). On the other hand, in characteristic 2, these covers may not be K3 surfaces, but are in general only integral, possibly even non-normal, Gorenstein surfaces with trivial dualizing sheaves ("K3-like"). In this talk, I will explain how some these results can been carried over to characteristic 2, even in case where the cover is not a K3 surface. This has striking consequences...