华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 4: 25 - 29

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.04.003

数学

论常模 Belyi 纤维化的分类 (英)

  • SOORI Atif Hasan ,
  • DAOUSSA Daniel
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  • 1. 华东师范大学 数学系，上海 200241; 2. 爱尔大学 数学系，伊斯兰堡 44000, 巴基斯坦

收稿日期: 2015-05-27

  网络出版日期: 2016-09-29

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On classification of isotrivial elliptic Belyi fibrations

  • SOORI Atif Hasan ,
  • DAOUSSA Daniel
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  • 1. Department of Mathematics, East China Normal University, Shanghai 200241, China; 2. Department of Mathematics, Air University, Islamabad 44000, Pakistan

Received date: 2015-05-27

  Online published: 2016-09-29

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摘要

本文对$\mathbb{P}^1$上带有三条奇异纤维的常模椭圆纤维化(简称Belyi纤维化)进行了分类， 给出了精确的12类带有截面的Belyi纤维化.作为这一分类的推论，还发现，除了一种情形外，其余情形对应的$\overline{\mathcal{M}}_1$中的轨迹都是零维的.

关键词： 椭圆纤维化; 常模; 相对极小; J - 不变量

本文引用格式

SOORI Atif Hasan , DAOUSSA Daniel . 论常模 Belyi 纤维化的分类 (英)[J]. 华东师范大学学报（自然科学版）, 2016 , 2016(4) : 25 -29 . DOI: 10.3969/j.issn.1000-5641.2016.04.003

Abstract

In this paper we classify relatively minimal, isotrivial families of curves $f: S \to \mathbb{P}^1$ of genus 1 with three singular fibers (Belyi fibrations). Assuming that these families have a section, we find that they are exactly 12 in number up to isomorphism. Moreover, as a result of this classification, we find that except one, the dimension of all other families in $\overline{\mathcal{M}}_1$ is zero.

Key words： elliptic fibrations; isotrivial; relatively minimal; J-invariant

参考文献

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[5] LU J, TAN S L. Inequalities between the Chern numbers of a singular fiber in a family of algebraic curves [J]. Trans Amer Math Soc, 2013, 365: 3373-3396.
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[ 9 ] TAN S L. Chern numbers of a singular fiber, modular invariants and isotrivial families of curves [J]. Acta Math Vietnam, 2010, 35: 159-172.

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