论文标题
$（10_3）$配置的单线扩展的模量空间
Moduli Spaces of One-Line Extensions of $(10_3)$ Configurations
论文作者
论文摘要
$ \ mathbb {cp}^2 $中的两行安排即使它们是组合同构的，也可以具有不同的拓扑属性。 Dan Cohen和Suciu的结果以及Randell的结果表明，在复杂共轭下可简化的模量空间是必要的条件。 我们提出了一种方法，可以制作许多组合线排列的示例，并从一组具有不可还原模量空间的示例中获得的可简化模量空间。 在本文中，我们确定了通过向十美元（10_3）$配置之一添加一条线来构建的11行的模量空间的降低性。在这个家族的四百九十五个组合线排列中，九十五具有可降低的模量空间，其中七十六是通过复杂共轭后的商后还原。
Two line arrangements in $\mathbb{CP}^2$ can have different topological properties even if they are combinatorially isomorphic. Results by Dan Cohen and Suciu and by Randell show that a reducible moduli space under complex conjugation is a necessary condition. We present a method to produce many examples of combinatorial line arrangements with a reducible moduli space obtained from a set of examples with irreducible moduli spaces. In this paper, we determine the reducibility of the moduli spaces of a family of arrangements of 11 lines constructed by adding a line to one of the ten $(10_3)$ configurations. Out of the four hundred ninety-five combinatorial line arrangements in this family, ninety-five have a reducible moduli space, seventy-six of which are still reducible after the quotient by complex conjugation.
