On the Torsion of Brieskorn Modules of Homogeneous Polynomials

Abstract

Let f ∈ C[X1,...,Xn] 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.