Analytic deviation of ideals and intersection theory of analytic spaces

In this note a stratification of analytic subspaces by analytic deviation of ideals is introduced and applied to define embedded components of an intersection (not necessarily proper) of complex analytic subspaces. Using the method of compact semi-analytic Stein neighbourhoods, a pointwise defined intersection multiplicity is proved to be constant along a dense Zariski open subset of such embedded components. For complex subspaces of a projective space one obtains precisely the distinguished varieties of intersection in the sense of Fulton and their intersection numbers.