Xiao's Conjecture on Canonically Fibered Surfaces
Algebraic Geometry
2017-09-13 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1405.5236,
title = {Xiao's Conjecture on Canonically Fibered Surfaces},
author = {Xi Chen},
journal= {arXiv preprint arXiv:1405.5236},
year = {2017}
}
Comments
47 pages, 2 figures