Resolution except for minimal singularities II. The case of four variables

Edward Bierstone, Pierre Lairez, Pierre D. Milman

Published 2011-07-27, updated 2011-08-18Version 2

In this sequel to Resolution except for minimal singularities I, we find the smallest class of singularities in four variables with which we necessarily end up if we resolve singularities except for normal crossings. The main new feature is a characterization of singularities in four variables which occur as limits of triple normal crossings singularities, and which cannot be eliminated by a birational morphism that avoids blowing up normal crossings singularities.