DEFORMATIONS OF POLYNOMIALS AND THEIR ZETA-FUNCTIONS

摘要

For an analytic in σ ∈(C, 0) family P_σ of polynomials in n variables a monodromy transformation h of the zero level set V_σ = {P_σ = 0} for sufficiently small σ ≠ 0 is denned. 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 give some examples of computations with the use of this technique.