On Kummer type construction of supersingular K3 surfaces in characteristic 2

We show that every supersingular K3 surface in characteristic 2 with Artin invariant less than or equal to 2 is obtained by the Kummer type construction of Schroeer.Comment: 18 pages, to appear in Pacific Journal of Mathematic

Canonical coverings of Enriques surfaces in characteristic 22

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 each configuration we describe which type of Enriques surfaces (classical or supersingular) appear as quotients of $\bar{Y}$.Comment: comments welcome / v2 (22 pages) contains several new results: the case of elliptic double point singularity is taken into consideration, and the description of 1-dimensional family of Enriques quotients is adde