For the signature of the Milnor fiber of a surface singularity of cyclic type, we prove a certain inequality, which naturally induce an answer of Durfee's conjecture in this case. For the proof, we use a certain perturbation method on the way of Hirzebruch's resolution process.
"Surface singularities on cyclic coverings and an inequality for the signature." J. Math. Soc. Japan 51 (2) 485 - 521, April, 1999. https://doi.org/10.2969/jmsj/05120485