On a conjecture by A. Durfee

摘要

We show how superisolated surface singularities can be used to find a counterexample to the following conjecture by A. Durfee [8]: for a complex polynomial f (x, y, z) in three variables vanishing at 0 with an isolated singularity there, "the local complex algebraic monodromy is of finite order if and only if a resolution of the germ ({ f = 0}, 0) has no cycles". A Zariski pair is given whose corresponding superisolated surface singularities, one has complex algebraic monodromy of finite order and the other not (answering a question by J. Stevens).