On atypical values and local monodromies of meromorphic functions

Abstract

A meromorphic function on a compact complex analytic manifold defines a $\bc\infty$ locally trivial fibration over the complement of a finite set in the projective line $\bc\bp^1$. We describe zeta-functions of local monodromies of this fibration around atypical values. Some applications to polynomial functions on $\bc^n$ are described.