In this paper we give full classification of rank 3 line arrangements in ${\mathbb{P}}^2$ (over a field of characteristic 0) that have a minimal logarithmic derivation of degree 3. The classification presents their defining polynomials, up to a change of variables, with their corresponding affine pictures. We also analyze the shape of such a logarithmic derivation, towards obtaining criteria for a line arrangement to possess a cubic minimal logarithmic derivation.

中文翻译：

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与生产线安排相关的对数推导

在本文中，我们对第3行的行排列进行了完全分类 ${\mathbb{P}}^{\mathrm{2个}}$（在特征0的字段上）具有最小对数3的对数导数。分类显示了其定义的多项式，直至变量的变化，以及它们的仿射图像。我们还分析了这种对数导数的形状，以期获得具有三次最小对数导数的线排列标准。