The Topological Zeta Function Associated to a Function on a Normal Surface Germ
نویسنده
چکیده
We associate to a regular function f on a normal surface germ (S; 0) an invariant, called the topological zeta function, which generalizes the same invariant for a plane curve germ; by deenition it is a rational function in one variable. We study its poles and their relation with the local monodromy of f , in particular we prove thègeneralized holomorphy conjecture'. We give a formula for this topological zeta function in terms of the log canonical model of (S; f ?1 f0g), and we also introduce a still more general invariant.
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