Generic residual intersections and intersection numbers of movable components

Abstract Given a sequence x of elements of a commutative equidimensional noetherian ring R , cycles z i ( x , R ) ( i ∈ N ) in the cycle group of polynomial rings over R are defined by generic residual intersections. The study of these cycles gives new insight into the theory for excess intersections in projective space developed by Stuckrad and Vogel, in particular concerning the contribution to the intersection cycle of embedded components not defined over the base field.