Counting Dirac braid relators and hyperelliptic Lefschetz fibrations
Counting Dirac braid relators and hyperelliptic Lefschetz fibrations
复制标题
计算狄拉克辫子相关器和超椭圆 Lefschetz 纤维振动
DOI：
10.1112/tlm3.12002
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
H. Endo and S. Kamada
中科院分区：
文献类型：
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作者：
H. Endo and S. Kamada
利用第二作者引入的图表描述方法，对闭定向曲面上的超椭圆Lefschetz纤维化定义了一个不变量，该不变量计算了monodromy中固有包含的Dirac辫的个数.作为应用，我们证明了给定基空间上亏格的两个超椭圆Lefschetz纤维化是稳定同构的当且仅当它们每种类型的奇异纤维的个数相同，且它们的奇性值相同.我们也给出了例子对超椭圆Lefschetz纤维具有相同数量的奇异纤维的每一种类型是不稳定同构的。
We define an invariantfor hyperelliptic Lefschetz fibrations over closed oriented surfaces, which counts the number of Dirac braids included intrinsically in the monodromy, by using chart description introduced by the second author. As an application, we prove that two hyperelliptic Lefschetz fibrations of genusover a given base space are stably isomorphic if and only if they have the same numbers of singular fibers of each type and they have the same value ofifis odd. We also give examples of pair of hyperelliptic Lefschetz fibrations with the same numbers of singular fibers of each type which are not stably isomorphic.