  The partition function of four-dimensional N=2 superconformal field theories
on S^4 computes the exact Kahler potential on the space of exactly marginal
couplings [1]. We present a new elementary proof of this result using
supersymmetry Ward identities. The partition function is a section rather than
a function, and is subject to ambiguities coming from Kahler transformations
acting on the Kahler potential. This ambiguity is realized by a local
supergravity counterterm in the underlying SCFT. We provide an explicit
construction of the Kahler ambiguity counterterm in the four dimensional N=2
off-shell supergravity theory that admits S^4 as a supersymmetric background.
