  We analyze the "eigenbundle" (localization bundle) of certain Hilbert modules
over bounded symmetric domains of rank $r,$ giving rise to complex-analytic
fibre spaces which are stratified of length $r+1.$ The fibres are described in
terms of K\"ahler geometry as line bundle sections over flag manifolds, and the
metric embedding is determined by taking derivatives of reproducing kernel
functions. Important examples are the determinantal ideals defined by vanishing
conditions along the various strata of the stratification.
