Bifurcations and topology of meromorphic germs

Abstract

A meromorphic germ at the origin in the complex space Cn is a ratio of two holomorphic germs on (Cn,0). After presentation of the basic definitions in the general context of arbitrary meromorphic germs the authors study the monodromy by calculating its zeta function. Then they give some results on homology splitting and bouquet-type theorems for the global case of meromorphic functions on compact complex manifolds. Some applications to traditional cases of rational functions on CPn, including in particular polynomial functions on Cn, are considered.