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.

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