Monodromies and Poincaré series of quasihomogeneous complete intersections (Q1766178)

In some special cases of plane curves or hypersurfaces singularities, a relation between the Poincaré series of the ring and the Saito dual of the reduced zeta function of the monodromy can be described [see for example \textit{S. M. Gusein-Zade, F. Delgado, A. Campillo}, J. Math. Sci., New York 105, No.2, 1839--1842 (2001); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat Obz. 68, 49--54 (1999; Zbl 1005.14012)]. The main result in this paper consists of giving a natural direct proof of the relation between the Poincaré series of the weighted homogeneous filtration of the ring of germs of functions on a quasi-homogeneous complete intersection to the Saito dual of the reduced zeta function of the classical monodromy transformations and the orbit invariants.