Modular invariants and singularity indices of hyperelliptic fibrations
Algebraic Geometry
2016-05-09 v1
Abstract
The modular invariants of a family of semistable curves are the degrees of the corresponding divisors on the image of the moduli map. The singularity indices were introduced by G. Xiao to classify singular fibers of hyperelliptic fibrations and to compute global invariants locally. In the semistable case, we show that the modular invariants corresponding with the boundary classes are just the singularity indices. As an application, we show that the formula of Xiao for relative Chern numbers is the same as that of Cornalba-Harris in the semistable case.
Keywords
Cite
@article{arxiv.1605.01803,
title = {Modular invariants and singularity indices of hyperelliptic fibrations},
author = {Xiao-Lei Liu},
journal= {arXiv preprint arXiv:1605.01803},
year = {2016}
}
Comments
To appear in Chin. Ann. Math. (B)