Abstract
A collection A = { D 1 , … , D n } of divisors on a smooth variety X is an arrangement if the intersection of every subset of A is smooth. We show that, if X is defined over a field of characteristic not equal to 2, a double cover of X ramified on an arrangement has a crepant resolution under additional hypotheses. Namely, we assume that all intersection components that change the canonical divisor when blown up are splayed , a property of the tangent spaces of the components first studied by Faber. This strengthens a result of Cynk and Hulek, which requires a stronger hypothesis on the intersection components. Further, we study the singular subscheme of the union of the divisors in A and prove that it has a primary decomposition where the primary components are supported on exactly the subvarieties which are blown up in the course of constructing the crepant resolution of the double cover.
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