  We describe, in the context of M-theory on elliptically fibered Calabi-yau
fourfolds, the change of variables that allow us to pass from the U(1)
invariant elliptic fibration to the one describing the uncompactified four
dimensional limit, where the U(1) symmetry is broken. These changes of
variables are the analog to the ones used to derive from the Atiyah-Hitchin
space the complex structure of the Seiberg-Witten solution for N=2
supersymmetric Yang-Mills. The connection between these changes of variables
and the recently introduced rotation of branes is discussed.
