Modular Invariants and Singularity Indices of Hyperelliptic Fibrations

被引：4

作者：

Liu, Xiaolei ^{[1
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100090, Peoples R China

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2016年 / 37卷 / 06期

关键词：

Modular invariants; Singularity indices; Moduli space of curves; CURVES;

D O I：

10.1007/s11401-016-1045-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The modular invariants of a family of curves are the degrees of the pullback of the corresponding divisors by the moduli map. The singularity indices were introduced by Xiao (1991) to classify singular fibers of hyperelliptic fibrations and to compute global invariants locally. In semistable case, the author shows that the modular invariants corresponding to the boundary divisor classes are just the singularity indices. As an application, the author shows that the formula of Xiao for relative Chern numbers is the same as that of Cornalba-Harris in semistable case.

引用

页码：875 / 890

页数：16

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