On complex homogeneous singularities

In this article, we consider the singularity of an arbitrary homogeneous polynomial with complex coefficients \(f(x_0,\dots,x_n)\) at the origin of \(\mathbb C^{n+1}\), via the study of the monodromy characteristic polynomials \(\Delta_l(t)\), and the relation between the monodromy zeta function and the Hodge spectrum of the singularity. We go further with \(\Delta_1(t)\) in the case \(n=2\). This work is based on knowledge of multiplier ideals and local systems.