In a recent paper, Cook et al. (Compos Math 154:2150–2194, 2018) used the splitting type of a line arrangement in the projective plane to study the number of conditions imposed by a general fat point of multiplicity j on the linear system of curves of degree \(j+1\) passing through the configuration of points dual to the given arrangement. If the number of conditions is less than the expected, they said that the configuration of points admits unexpected curves. In this paper, we characterize supersolvable line arrangements whose dual configuration admits unexpected curves and we provide other infinite families of line arrangements with this property.

中文翻译：

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特殊线路布置产生意外的曲线

在最近的一篇论文中，Cook等人。（Compos Math 154：2150–2194，2018）使用投影平面中线布置的分割类型来研究度为\（j +的线性系统上的多重性j的一般胖点所施加的条件数1 \）传递给定排列的对偶点的配置。如果条件数少于预期，他们说点的配置允许出现意外的曲线。在本文中，我们描述了超可解线的布置，其双重配置允许出现意外曲线，并且我们提供了具有此属性的其他无限系列的线。