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.