A Compactification of Open Varieties

الأصل · EN

In this paper we show a general method to compactify certain open varieties by adding normal crossing divisors. This is done by proving that blowing up along an arrangement of subvarieties can be carried out. Important examples such as Ulyanov's configuration spaces, spaces of holomorphic maps, etc., are covered. Intersection ring and (non-recursive) Hodge polynomails are computed. Further general structures arising from the blowup process are described and studied.