A compactification of open varieties

In this paper we prove a general method to compactify certain open varieties by adding normal crossing divisors. This is done by showing that blowing up along an arrangement of subvarieties can be carried out. Important examples such as Ulyanov's configuration spaces and complements of arrangements of linear subspaces in projective spaces, etc., are covered. Intersection ring and (nonrecursive) Hodge polynomials are computed. Furthermore, some general structures arising from the blowup process are also described and studied.