2014/05/20 by Xi Chen, Chen, Xi · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1405.5236
A canonically fibered surface is a surface whose canonical series maps it to a curve. Using Miyaoka-Yau inequality, A. Beauville proved that a canonically fibered surface has relative genus at most 5 when its geometric genus is sufficiently large. G. Xiao further conjectured that the relative genus cannot exceed 4. We give a proof of this conjecture.