On the Torsion of Brieskorn Modules of Homogeneous Polynomials

Abstract

Let $f\in \mathbb{C}[X_1,...,X_n]$ be a homogeneous polynomial and $B(f)$ be the corresponding Brieskorn module. We describe the torsion of the Brieskorn module $B(f)$ for $n=2$ and show that any torsion element has order $1$. For $n>2$, we find some examples in which the torsion order is strictly greater than $1$.