Resolution of singularities of pairs preserving semi-simple normal crossings

Let X denote a reduced algebraic variety and D a Weil divisor on X . The pair ( X , D ) is said to be semi-simple normal crossings (semi-snc) at if X is simple normal crossings at a (i.e., a simple normal crossings hypersurface, with respect to a local embedding in a smooth ambient variety), and D is induced by the restriction to X of a hypersurface that is simple normal crossings with respect to X . We construct a composition of blowings-up such that the transformed pair is everywhere semi-simple normal crossings, and f is an isomorphism over the semi-simple normal crossings locus of ( X , D ). The result answers a question of Kollár.