  We prove a perturbative inversion theorem for the map between the interacting
and the noninteracting Fermi surface for a class of many fermion systems with
strictly convex Fermi surfaces and short-range interactions between the
fermions. This theorem gives a physical meaning to the counterterm function K
that we use in the renormalization of these models: K can be identified as that
part of the self--energy that causes the deformation of the Fermi surface when
the interaction is turned on.
