Slope equality of plane curve fibrations and its application to Durfee’s conjecture

Abstract

We give a slope equality for fibered surfaces whose general fiber is a smooth plane curve. As a corollary, we prove a Durfee-type inequality for isolated hypersurface surface singularities, which implies Durfee's strong conjecture for such singularities with non-negative topological Euler number of the exceptional set of the minimal resolution.