  Warped compactifications with branes provide a new approach to the hierarchy
problem and generate a diversity of four-dimensional thresholds. We investigate
the relationships between these scales, which fall into two classes.
Geometrical scales, such as thresholds for Kaluza-Klein, excited string, and
black hole production, are generically determined soley by the spacetime
geometry. Dynamical scales, notably the scale of supersymmetry breaking and
moduli masses, depend on other details of the model. We illustrate these
relationships in a class of solutions of type IIB string theory with imaginary
self-dual fluxes. After identifying the geometrical scales and the resulting
hierarchy, we determine the gravitino and moduli masses through explicit
dimensional reduction, and estimate their value to be near the four-dimensional
Planck scale. In the process we obtain expressions for the superpotential and
Kahler potential, including the effects of warping. We identify matter living
on certain branes to be effectively sequestered from the supersymmetry breaking
fluxes: specifically, such "visible sector" fields receive no tree-level masses
from the supersymmetry breaking. However, loop corrections are expected to
generate masses, at the phenomenologically viable TeV scale.
