Dedekind sums and the signature of \(f(x,y)+z^N\)
There is a relatively long-standing conjecture of Durfee, stating that the signature of the Milnor fiber of an isolated complete intersection is negative. Even stronger, he conjectured the inequality \(p_g \leq \mu/6\), where \(p_g\) is the geometric genus, and \(\mu\) the Milnor number. In this paper the author proves this inequality for singularities of type \(f(x,y) + z^N,\) where \(f\) defines an irreducible plane curve singularity. Its proof uses generalized Dedekind sums associated to the embedded resolution of \(f\).
scientific article; zbMATH DE number 1206723