On the monodromy of a plane curve singularity and the Poincaré series of its ring of functions
Let \(f:(\mathbb{C}^2 , 0) \rightarrow (\mathbb{C}, 0)\) be the germ of a holomorphic function with an isolated critical point at the origin and let \((C, 0)\) be the irreducible plane curve singularity defined by \(f = 0\). Let \(V_{f}\) be the Milnor fiber of the singularity and let \(h_{f}: V_{f} \rightarrow V_{f}\) be the monodromy transformation. Let \(\zeta_{f}(t)\) be the zeta function of \(h_{f}\), as defined by \textit{N. A'Campo} [Comment. Math. Helv. 50, 233-248 (1975; Zbl 0333.14008)]. In this paper the authors prove that \(\zeta_{f}(t)\) is exactly the Poincaré series of the ring of functions of \(C\).
scientific article; zbMATH DE number 1407615