Asian Journal of Mathematics

Volume 26 (2022)

Number 1

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

Pages: 119 – 136



Makoto Enokizono (Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, Japan)


We give a slope equality for fibered surfaces whose general fiber is a smooth plane curve. As a corollary, we prove a “strong” 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.


fibered surface, plane curve, local signature, hypersurface singularity

2010 Mathematics Subject Classification


Received 30 September 2019

Accepted 15 September 2021

Published 30 January 2023