On complex homogeneous singularities

Abstract

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.