Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at $$t=-1$$ t = - 1
Generators for the hyperelliptic Torelli group and the kernel of the Burau representation at $$t=-1$$ t = - 1
复制标题
超椭圆 Torelli 群的生成器和 $$t=-1$$ t = - 1 处 Burau 表示的内核
DOI：
10.1007/s00222-014-0537-9
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发表时间：
2014
影响因子：
3.1
通讯作者：
Brendle T
中科院分区：
文献类型：
--
作者：
Brendle T
证明了超椭圆Torelli群是由超椭圆对合所保持的分离曲线的Dehn扭生成的。这验证了海恩的一个猜想。超椭圆Torelli群可以等同于在的Burau表示的核，也可以等同于周期映射的分支轨迹的基本群，因此我们得到了它们的类似生成集。一个应用是，超椭圆曲线轨迹的Torelli空间中的每个分量在紧致型曲线相加时变为单连通。
We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating curves that are preserved by the hyperelliptic involution. This verifies a conjecture of Hain. The hyperelliptic Torelli group can be identified with the kernel of the Burau representation evaluated atand also the fundamental group of the branch locus of the period mapping, and so we obtain analogous generating sets for those. One application is that each component in Torelli space of the locus of hyperelliptic curves becomes simply connected when curves of compact type are added.