This note gives the complete projective classification of rational, cuspidal plane curves of degree at least 6, and having only weighted homogeneous singularities. It also sheds new light on some previous characterizations of free and nearly free curves in terms of Tjurina numbers. Finally, we suggest a stronger form of Terao’s conjecture on the freeness of a line arrangement being determined by its combinatorics.

中文翻译：

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关于有理尖面曲线和雅可比环的局部上同调

本注释给出了阶数至少为 6 且仅具有加权齐次奇点的有理尖面曲线的完整射影分类。它还揭示了先前根据 Tjurina 数对自由曲线和几乎自由曲线进行的一些表征。最后，我们提出了一种更强形式的 Terao 猜想，即由其组合学决定的线排列的自由度。