We start the study of reduced complex projective plane curves, whose Jacobian syzygy module has 3 generators. Among these curves one finds the nearly free curves introduced by the authors, and the plus-one generated line arrangements introduced by Takuro Abe. All the Thom–Sebastiani type plane curves, and more generally, any curve whose global Tjurina number is equal to a lower bound given by A. du Plessis and C.T.C. Wall, are 3-syzygy curves. Rational plane curves which are nearly cuspidal, i.e. which have only cusps except one singularity with two branches, are also related to this class of curves.

中文翻译：

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具有三个合子的平面曲线、最小 Tjurina 曲线和近尖点曲线

我们开始研究简化的复杂投影平面曲线，其 Jacobian syzygy 模块有 3 个生成器。在这些曲线中，可以找到作者介绍的几乎自由的曲线，以及 Takuro Abe 介绍的加一生成线排列。所有 Thom-Sebastiani 型平面曲线，更一般地说，全局 Tjurina 数等于 A. du Plessis 和 CTC Wall 给出的下界的任何曲线都是 3-syzygy 曲线。有理平面曲线接近尖点，即除了一个奇点和两个分支外只有尖点，也与这类曲线有关。