华东师范大学学报(自然科学版)

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论常模 Belyi 纤维化的分类 (英)

SOORI Atif Hasan[1,2] ,DAOUSSA Daniel[1]   

  1. 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 出版日期:2016-07-25 发布日期:2016-09-29
  • 通讯作者: SOORI Atif Hasan, 男, 博士研究生, 研究方向为代数几何. E-mail: ah.soori@yahoo.com.

On classification of isotrivial elliptic Belyi fibrations

SOORI Atif Hasan[1,2] ,DAOUSSA Daniel[1]   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200241, China; 2. Department of Mathematics, Air University, Islamabad 44000, Pakistan
  • Received:2015-05-27 Online:2016-07-25 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

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