Geodesic
On Atypical Values and Local Monodromies of Meromorphic Functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Solitons, geometry, and topology: on the crossroads, Tome 225 (1999), pp. 168-176.

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A meromorphic function on a compact complex analytic manifold defines a $C^\infty$ locally trivial fibration over the complement to a finite set in the projective line $\mathbb{CP}^1$ – the bifurcation set. Loops around points of the bifurcation set give rise to corresponding monodromy transformations of this fibration. We show that the zeta-functions of these monodromy transformations can be expressed in local terms, namely, as integrals of zeta-functions of meromorphic germs with respect to the Euler characteristic. A particular case of meromorphic functions on the projective space $\mathbb{CP}^n$ are those defined by polynomial functions of $n$ variables. We describe some applications of this technique to polynomial functions. 
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S. M. Gusein-Zade; I. Luengo; A. Melle-Hernández. On Atypical Values and Local Monodromies of Meromorphic Functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Solitons, geometry, and topology: on the crossroads, Tome 225 (1999), pp. 168-176. http://geodesic.mathdoc.fr/item/TM_1999_225_a10/

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