sentences:  The definition of this is made such that making this choice is meaningful, giving smooth centers transversal to the exceptional divisors.In either case the problem is reduced to resolve singularities of the tuple formed by the ideal sheaf and the extra data (the exceptional divisors and the order, "d", to which the resolution should go for that ideal).This tuple is called a "marked ideal" and the set of points in which the order of the ideal is larger than "d" is called its co-support.