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

2017/04/28 by Makoto Enokizono, Enokizono, Makoto
Mathematics · #14D06 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1704.08806

openalex publication_date 2017/04/28 · openalex created_date 2023/01/31 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Durfee-type inequality for hypersurface surface singularities
• Slope inequality for families of curves over surfaces
• Slope inequality of fibered surfaces, Morsification conjecture and moduli of curves
• Upper bounds on the slope of certain fibered surfaces
• Slope equalities for genus 5 surface fibrations