  For an analytic family P_s of polynomials in n variables (depending on a
complex number s, and defined in a neighborhood of s = 0), there is defined a
monodromy transformation h of the zero level set V_s= {P_s=0} for s different
from 0, small enough. The zeta function of this monodromy transformation is
written as an integral with respect to the Euler characteristic of the
corresponding local data. This leads to a study of deformations of holomorphic
germs and their zeta functions. We show some examples of computations with the
use of this technique.
