Plane curves with three syzygies, plus-one generated curves, and nearly cuspidal curves
Résumé
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 recently by Takuro Abe. Rational plane curves which are nearly cuspidal, i.e. which have only cusps except one singularity with two branches, are also related to these classes of curves.